user145: Non-self (anātman) and emptiness (śūnya or śūnyatā) are very similar aspects of the Truth of Suffering. So similar that they are hard to distinguish apart. What is the difference between them? (Or what is purpose to have them as separate characteristics?)
Update: I did not specified that answers should be from Mahayana perspective, assuming that Theravada have the same list of 16 Aspects of Noble Truths, but it seems that Theravada list is quite different (see Visiddhimagga). And for some reason most answers was from Theravada perspective. I don't want to disregard Theravada explanations, and welcome them. But in Theravada, it seems, that suññata and anatta are never enumerated in the same list. Thus they don't imply distinction, and it's is quite possible that they are just synonyms (as pointed out by Unrul3r).
I will quote Abhidharmasamuccaya for more context:

What are the general characteristics of suffering? They are the
characteristics of (1) impermanence (anitya), (2) suffering (duḥkha),
(3) emptiness (śūnya) and (4) non-self (anātma).

Thus it's established that these are different characteristics.
Further Asanga provides some elaborations:

(3) What is the characteristic of emptiness (śūnyatā)? It is the
non-existence (abhāva) of a certain thing, there. To see
(samanupaśyanā) in this way is emptiness. Again, it is the existence
(bhāva) of another thing, there. In this way there is true knowledge
(yathābhūtajñāna). This is called emptiness perceived by penetration
(avatāra). True knowledge denotes the informed meaning. What is the
meaning of the non-existence of a certain thing, there? It is the
non-existence in the aggregates, elements and spheres of a self or
anything whatsoever belonging to a self of permanent, durable,
eternal, immutable nature. In this way is their emptiness. What is the
meaning of the existence of another thing, there? It is the fact that
there is non-self in the aggregates, elements and spheres. It is the
nonexistence of the self, and the existence of the non-self. It is in
this sense that the Blessed One has said: ‘Existence is the true
knowledge of an existent thing; non-existence is the true knowledge of
a non-existent thing.’
(4) What is the characteristic of non-self (anātma)? It is the
non-existence in the aggregates, elements and spheres of the
characteristics postulated in the theory of the self (ātmavāda) as a
result of the nonexistence of the characteristics of a self in the
aggregates, elements and spheres. This is called the characteristic of
non-self. For this reason the Blessed One said: ‘All things (dharmas)
are without self.’122 Furthermore, the Blessed One has said: “(i) All
of that is not mine, (ii) nor ‘I am’ nor my self”.123

So in light of this, what is the difference?

user92: 1. What is the difference between them?
As far as I know, there is no difference. The world is said to be empty of self and what belongs to self.

Then the Venerable Ānanda approached the Blessed One … and said to
  him: “Venerable sir, it is said, ‘Empty is the world, empty is the
  world.’ In what way, venerable sir, is it said, ‘Empty is the world’?”
“It is, Ānanda, because it is empty of self and of what belongs to
  self that it is said, ‘Empty is the world.’ And what is empty of self
  and of what belongs to self? The eye, Ānanda, is empty of self and of
  what belongs to self. Forms are empty of self and of what belongs to
  self. Eye-consciousness is empty of self and of what belongs to self.
  Eye-contact is empty of self and of what belongs to self…. Whatever
  feeling arises with mind-contact as condition—whether pleasant or
  painful or neither-painful-nor-pleasant—that too is empty of self and
  of what belongs to self.
“It is, Ānanda, because it is empty of self and of what belongs to
  self that it is said, ‘Empty is the world.’”
  -SN 35.85, World Emptiness (Suñña­ta­loka­-sutta)



Mogharaja: Twice now, O Sakyan, I've asked you, but you, O One with
  Eyes, haven't answered me. "When asked the third time, the divine seer
  answers": so I have heard. This world, the next world, the Brahma
  world with its devas: I don't know how they're viewed by the glorious
  Gotama. So to the one who has seen to the far extreme, I've come with
  a question: One who regards the world in what way isn't seen by
  Death's King?
The Buddha: Always mindful, Mogharaja, regard the world as empty,
  having removed any view in terms of self. This way one is above and
  beyond death. One who regards the world in this way isn't seen by
  Death's King.
  -Sn 5.15, Mogharaja's Question (Mogharāja-māṇava-pucchā)

This is not the only meaning of emptiness in the early texts though.

user111: They are not the same. But Suñña is one aspect of Anatta.
Suñña can mean devoid of any inherent value, goodness or a soul.
Anatta means not under one's control.
Something that is Anatta isn't always Suñña. ex: Nibbana.
Nibbana is peaceful, devoid of suffering and permanent. So there's goodness to it. But it's still not a self or a soul since it's not under your control.
There are 40 meditative objects described in Patisambidhamagga under Vipassana meditation.
Ten kinds from the view-point of anicca; 
twenty-five kinds from the view-point of dukkha; 
five kinds from the view-point of anatta. 
Suñña is one of those 40.
The detailed explanations are in Visuddhimagga. 

user415: I'm new here, thus have not acquired enough points to add my comments above, so I'll do so here. But I agree with the thrust. 
I'll sharpen my answer by saying right off the top there is no difference between non-self and emptiness. They are one and the same thing. To comprehend emptiness you will already comprehend non-self, just different ways of looking at reality. Different vantage points.
Emptiness is the key concept in Buddhism. It lies behind everything in Buddhism. If a thing is empty it has no permanent substance. Why? Because it is always in transition, is in the midst of change, is not immutable. If it is in constant change it cannot satisfy, is therefore dukkha, suffering. We the observer are also in the midst of constant change, and therefore share the same characteristic this discussion began with — we are also empty. (Despite all appearances to the contrary.) 
These three are the three characteristics of all phenomena. Everything is not only subject to change, but that change is constant. Anicca. Everything ultimately cannot satisfy. Dukkha. There is no permanent reference point, no self. Anatta. 
The questioner makes an almost inevitable error. He/she assumes the puzzle of emptiness can be understood analytically, rationally. That by breaking it down into its parts and coming to understand each in turn, assemble a comprehensive understanding. It can't be done.
The only way is to confront it all at once, as a whole. Proceed by looking at what changes. I say that includes anything and everything. Am I right or am I wrong? Can you identify anything that is lasting? Perhaps a rock or a mountain. But these change as well, although not rapidly. Even a mountain is rising and/or falling. 
Everywhere you turn there is impermanence. Everything is in process. Everything IS process. 
I'll respond in your comments to the above.

user10319: When we look for "impermanence" we find only a single instant - hence "impermanence" (the process of change from  moment to moment in the form of a "continuity" comprised of past, present, and future) is not there. (There is no continuity as there is only a single instant).
When, within that single instant, we look for a thing, we find only non-thing parts - hence, that so-called "thing" is not there. 
And when we look at those parts referred to as "self" in the theory of self, we find that each of them is not self - hence, that so-called "self" is not there.
And since none of those parts is "self", neither can any part be owned by a self - because there is no self there which could own any part.

user16: I would add to this, that in the reception of these two terms, there is a difference. While the two terms are possibly used synonymously in the second sermon of the Buddha (compare the answers already given for this), the terminus technicus in early buddhism is anattā/anātman, being as one of the three marks of existence a claim of the Buddha which marks the uncoupling of Buddhism from the philosophical mainstream of that time.
The word(s) suñña/śūnya have acquired a more refined philosophical sense, since they were to a great extent 'popularized' by Nagarjuna and the Śūnyatāvāda school of early Mahayana. In his main work Mūlamadhyamakakārikā Nagarjuna does in a (philosophically) much more thorough way than was done by the Buddha dissect certain supposed elements of existence, proving, that they are empty. By and large this is in response to the rival buddhist ontologies (Sarvastivada and Sautrantika) and in the end more or less re-states what the Buddha had already stated: anattā/anātman, but on a much more sound philosophical and argumentative basis. (By the way: it reiterates also the Buddha's contempt for metaphysics)
In short: In discourse, anattā/anātman makes one think of Buddhism and the Buddha, while suñña/śūnya incites more special associations to Nagarjuna and his school.
Please note, that the adjectives used in comparison of the words of the Buddha and Nagarjuna in no way constitute value-judgements. They just indicate, that Nagarjuna responded to different needs and not, that what he said is worth more.

user43: As I understand, Mahayana's shunyata (noun, because shunya is adjective) includes all Three Characteristics of Existence, as well as Nirvana (sometimes counted as the fourth!)
In this sense, Shunyata is the all-encompassing view, and as close as it gets to Ultimate Truth, while Anatta is but one aspect of this truth.

145: <p>Non-self (<em>anātman</em>) and emptiness (<em>śūnya</em> or <em>śūnyatā</em>) are very similar <a href="http://www.chinabuddhismencyclopedia.com/en/index.php?title=Sixteen_Aspects_of_the_Four_Noble_Truths" rel="noreferrer">aspects of the Truth of Suffering</a>. So similar that they are hard to distinguish apart. What is the <em>difference</em> between them? (Or what is purpose to have them as separate characteristics?)</p>
<p><strong>Update</strong>: I did not specified that answers should be from Mahayana perspective, assuming that Theravada have the same list of <em>16 Aspects of Noble Truths</em>, but it seems that Theravada list is quite different (see Visiddhimagga). And for some reason most answers was from Theravada perspective. I don't want to disregard Theravada explanations, and welcome them. But in Theravada, it seems, that <em>suññata</em> and <em>anatta</em> are never enumerated in the same list. Thus they don't imply distinction, and it's is quite possible that they are just synonyms (<a href="https://buddhism.stackexchange.com/a/1885/145">as pointed out by Unrul3r</a>).</p>
<p>I will quote <em>Abhidharmasamuccaya</em> for more context:</p>
<blockquote>
<p><strong>What are the general characteristics of suffering?</strong> They are the
characteristics of (1) impermanence (anitya), (2) suffering (duḥkha),
(3) emptiness (śūnya) and (4) non-self (anātma).</p>
</blockquote>
<p>Thus it's established that these are different characteristics.</p>
<p>Further Asanga provides some elaborations:</p>
<blockquote>
<p>(3) <strong>What is the characteristic of emptiness (śūnyatā)?</strong> It is the
non-existence (abhāva) of a certain thing, there. To see
(samanupaśyanā) in this way is emptiness. Again, it is the existence
(bhāva) of another thing, there. In this way there is true knowledge
(yathābhūtajñāna). This is called emptiness perceived by penetration
(avatāra). True knowledge denotes the informed meaning. What is the
meaning of the non-existence of a certain thing, there? It is the
non-existence in the aggregates, elements and spheres of a self or
anything whatsoever belonging to a self of permanent, durable,
eternal, immutable nature. In this way is their emptiness. What is the
meaning of the existence of another thing, there? It is the fact that
there is non-self in the aggregates, elements and spheres. It is the
nonexistence of the self, and the existence of the non-self. It is in
this sense that the Blessed One has said: ‘Existence is the true
knowledge of an existent thing; non-existence is the true knowledge of
a non-existent thing.’</p>
<p>(4) <strong>What is the characteristic of non-self (anātma)?</strong> It is the
non-existence in the aggregates, elements and spheres of the
characteristics postulated in the theory of the self (ātmavāda) as a
result of the nonexistence of the characteristics of a self in the
aggregates, elements and spheres. This is called the characteristic of
non-self. For this reason the Blessed One said: ‘All things (dharmas)
are without self.’122 Furthermore, the Blessed One has said: “(i) All
of that is not mine, (ii) nor ‘I am’ nor my self”.123</p>
</blockquote>
<p>So in light of this, what is the <em>difference</em>?</p>
 92: <h2>1. What is the difference between them?</h2>

<p>As far as I know, there is no difference. The world is said to be <em>empty of self</em> and <em>what belongs to self</em>.</p>

<blockquote>
  <p>Then the Venerable Ānanda approached the Blessed One … and said to
  him: “Venerable sir, it is said, ‘Empty is the world, empty is the
  world.’ In what way, venerable sir, is it said, ‘Empty is the world’?”</p>
  
  <p>“It is, Ānanda, because it is <strong>empty of self and of what belongs to
  self</strong> that it is said, ‘Empty is the world.’ And what is empty of self
  and of what belongs to self? The eye, Ānanda, is empty of self and of
  what belongs to self. Forms are empty of self and of what belongs to
  self. Eye-consciousness is empty of self and of what belongs to self.
  Eye-contact is empty of self and of what belongs to self…. Whatever
  feeling arises with mind-contact as condition—whether pleasant or
  painful or neither-painful-nor-pleasant—that too is empty of self and
  of what belongs to self.</p>
  
  <p>“It is, Ānanda, because it is empty of self and of what belongs to
  self that it is said, ‘Empty is the world.’”<br>
  -<a href="http://suttacentral.net/pi/sn35.85" rel="nofollow"><em>SN 35.85, World Emptiness (Suñña­ta­loka­-sutta)</em></a></p>
</blockquote>

<hr>

<blockquote>
  <p><em>Mogharaja:</em> Twice now, O Sakyan, I've asked you, but you, O One with
  Eyes, haven't answered me. "When asked the third time, the divine seer
  answers": so I have heard. This world, the next world, the Brahma
  world with its devas: I don't know how they're viewed by the glorious
  Gotama. So to the one who has seen to the far extreme, I've come with
  a question: One who regards the world in what way isn't seen by
  Death's King?</p>
  
  <p><em>The Buddha:</em> Always mindful, Mogharaja, <strong>regard the world as empty,
  having removed any view in terms of self</strong>. This way one is above and
  beyond death. One who regards the world in this way isn't seen by
  Death's King.<br>
  -<a href="http://www.accesstoinsight.org/tipitaka/kn/snp/snp.5.15.than.html" rel="nofollow"><em>Sn 5.15, Mogharaja's Question (Mogharāja-māṇava-pucchā)</em></a></p>
</blockquote>

<p>This is not the only meaning of emptiness in the early texts though.</p>
 111: <p>They are not the same. But Suñña is one aspect of Anatta.
Suñña can mean devoid of any inherent value, goodness or a soul.
Anatta means not under one's control.
Something that is Anatta isn't always Suñña. ex: Nibbana.
Nibbana is peaceful, devoid of suffering and permanent. So there's goodness to it. But it's still not a self or a soul since it's not under your control.</p>

<p>There are 40 meditative objects described in Patisambidhamagga under Vipassana meditation.
Ten kinds from the view-point of anicca; 
twenty-five kinds from the view-point of dukkha; 
five kinds from the view-point of anatta. 
Suñña is one of those 40.
The detailed explanations are in Visuddhimagga. </p>
 415: <p>I'm new here, thus have not acquired enough points to add my comments above, so I'll do so here. But I agree with the thrust. </p>

<p>I'll sharpen my answer by saying right off the top there is no difference between non-self and emptiness. They are one and the same thing. To comprehend emptiness you will already comprehend non-self, just different ways of looking at reality. Different vantage points.</p>

<p>Emptiness is the key concept in Buddhism. It lies behind everything in Buddhism. If a thing is empty it has no permanent substance. Why? Because it is always in transition, is in the midst of change, is not immutable. If it is in constant change it cannot satisfy, is therefore dukkha, suffering. We the observer are also in the midst of constant change, and therefore share the same characteristic this discussion began with — we are also empty. (Despite all appearances to the contrary.) </p>

<p>These three are the three characteristics of all phenomena. Everything is not only subject to change, but that change is constant. Anicca. Everything ultimately cannot satisfy. Dukkha. There is no permanent reference point, no self. Anatta. </p>

<p>The questioner makes an almost inevitable error. He/she assumes the puzzle of emptiness can be understood analytically, rationally. That by breaking it down into its parts and coming to understand each in turn, assemble a comprehensive understanding. It can't be done.</p>

<p>The only way is to confront it all at once, as a whole. Proceed by looking at what changes. I say that includes anything and everything. Am I right or am I wrong? Can you identify anything that is lasting? Perhaps a rock or a mountain. But these change as well, although not rapidly. Even a mountain is rising and/or falling. </p>

<p>Everywhere you turn there is impermanence. Everything is in process. Everything IS process. </p>

<p>I'll respond in your comments to the above.</p>
 10319: <p>When we look for "impermanence" we find only a single instant - hence "impermanence" (the process of change from  moment to moment in the form of a "continuity" comprised of past, present, and future) is not there. (There is no continuity as there is only a single instant).</p>

<p>When, within that single instant, we look for a thing, we find only non-thing parts - hence, that so-called "thing" is not there. </p>

<p>And when we look at those parts referred to as "self" in the theory of self, we find that each of them is not self - hence, that so-called "self" is not there.</p>

<p>And since none of those parts is "self", neither can any part be owned by a self - because there is no self there which could own any part.</p>
 16: <p>I would add to this, that in the reception of these two terms, there is a difference. While the two terms are possibly used synonymously in the second sermon of the Buddha (compare the answers already given for this), the <em>terminus technicus</em> in early buddhism is <em>anattā/anātman</em>, being as one of the three marks of existence a claim of the Buddha which marks the uncoupling of Buddhism from the philosophical mainstream of that time.</p>

<p>The word(s) <em>suñña/śūnya</em> have acquired a more refined philosophical sense, since they were to a great extent 'popularized' by Nagarjuna and the <em>Śūnyatāvāda</em> school of early Mahayana. In his main work <em>Mūlamadhyamakakārikā</em> Nagarjuna does in a (philosophically) much more thorough way than was done by the Buddha dissect certain supposed elements of existence, <strong>proving</strong>, that they are empty. By and large this is in response to the rival buddhist ontologies (Sarvastivada and Sautrantika) and in the end more or less re-states what the Buddha had already stated: <em>anattā/anātman</em>, but on a much more sound philosophical and argumentative basis. (By the way: it reiterates also the Buddha's contempt for metaphysics)</p>

<p>In short: In discourse, <em>anattā/anātman</em> makes one think of Buddhism and the Buddha, while <em>suñña/śūnya</em> incites more special associations to Nagarjuna and his school.</p>

<p><em>Please note, that the adjectives used in comparison of the words of the Buddha and Nagarjuna in no way constitute value-judgements. They just indicate, that Nagarjuna responded to different needs and not, that what he said is worth more.</em></p>
 43: <p>As I understand, Mahayana's <em>shunyata</em> (noun, because <em>shunya</em> is adjective) includes all Three Characteristics of Existence, as well as Nirvana (sometimes counted as the fourth!)</p>

<p>In this sense, Shunyata is the all-encompassing view, and as close as it gets to Ultimate Truth, while Anatta is but one aspect of this truth.</p>
