user2493: I've heard both of these Pali terms translated to the English term "effort".
1: sammā-vāyāma: the 6th item in the 8-fold path.
2: virya: the 2nd of the 5 faculties/powers/Indrias.
If 2 terms are used instead of 1, they probably represent slightly different concepts but the similarity and difference between these 2 is unclear to me.
My best guess from my fuzzy understanding is ...
Gil Fronsdal has identified virya as being a kind of "heroic effort".
It's part of the 5 Indrias and Indra was the god that ruled the other gods so perhaps this refers to an heroic effort to rule over the hindrances?
sammā-vāyāma is associated with the 4 right exertions.
As such it seems to be about moving away from unwholesome states and towards wholesome states.
The 2 terms seem very similar.
The only difference I can detect is that the "heroic" modifier associated with virya suggests a stronger emphasis on courage and/or aggression.
Is this correct?

user16297: samma padhana (right exertion from 37 bodhi pakkhiya), viriya-indriya, viriya sambojjhanga (of 7 awakening factors), samma vayamo (right effort of noble eightfold path) are equivalent. The slightly different official definition for each term, is meant to highlight a particular aspect of right effort.
You'll notice in the right effort definition (SN 45.8), all of those words are found in the formula (vayamati/vayamo, viriya, padahati/padhana). 
Another word that frequently occurs in the suttas, such as in the satipatthana formula, 'ātāpi' (ardency), is a code word that also means the same right effort formula (see AN 4.14 verse at end)
http://lucid24.org/an/an04/an04-0014/index.html

user8157: Their contextual use in the suttas is the same, as follows:

And what is right effort? Katamo ca, bhikkhave, sammāvāyāmo?
It’s when a mendicant generates enthusiasm, tries, makes an effort,
  exerts the mind, and strives so that bad, unskillful qualities don’t
  arise. Idha, bhikkhave, bhikkhu anuppannānaṃ pāpakānaṃ akusalānaṃ
  dhammānaṃ anuppādāya chandaṃ janeti vāyamati vīriyaṃ ārabhati cittaṃ
  paggaṇhāti padahati,
SN 45.8

And what is the faculty of energy? Katamañca, bhikkhave,
  vīriyindriyaṃ?
It’s when a mendicant lives with energy roused up for giving up
  unskillful qualities and embracing skillful qualities. They’re strong,
  staunchly vigorous, not slacking off when it comes to developing
  skillful qualities. Idha, bhikkhave, ariyasāvako āraddhavīriyo
  viharati akusalānaṃ dhammānaṃ pahānāya, kusalānaṃ dhammānaṃ
  upasampadāya, thāmavā daḷhaparakkamo anikkhittadhuro kusalesu dhammesu.
They generate enthusiasm, try, make an effort, exert the mind, and
  strive so that bad, unskillful qualities don’t arise. So anuppannānaṃ
  pāpakānaṃ akusalānaṃ dhammānaṃ anuppādāya chandaṃ janeti vāyamati
  vīriyaṃ ārabhati cittaṃ paggaṇhāti padahati
SN 48.10

The word 'vāyāma' is derived from 'vi + ā + yam' where 'yam' or 'yāma' appears to mean 'restraint', 'don't do', 'reining in' or 'control'. One fluent in Pali will need to explain how 'vi + ā' modify 'yāma'.  
The word 'viriya' I guess is derived from 'vīra + ya' and is said to literally mean 'state of a strong man'. 'Vīra' means 'strong', 'brave' or 'heroic' thus 'ya' must mean 'state'. 
Therefore, merely guessing, 'viriya' appears to be a 'thing', namely, 'energy'; where as 'vāyāma' appears related to acting or related to a verb, i.e., possibly a 'verbal noun'. In other words, in the Pali above, there is the phrase 'vāyamati vīriyaṃ'. Here, 'vāyamati' (due to ending in 'ati') is a verb; where as 'vīriyaṃ' is a noun. Thus, the phrase 'vāyamati vīriyaṃ' appears to mean: 'to exercise energy' or 'to exert energy'.  
In summary, 'vayama' appears related to the action of acting; where as 'viriya' appears related to the quality of acting. This said, I could be wrong, here, because I am merely guessing. 

user13709: Sometimes a look at opposite terms can help.
For avāyāmaṃ we have weakly directed effort:

SN11.1:3.3: without working for it or trying hard—

For avīriyā we have apathetic lethargy:

MN60:21.7: All sentient beings, all living creatures, all beings, all souls lack control, power, and energy. Molded by destiny, circumstance, and nature, they experience pleasure and pain in the six classes of rebirth.’


2493: <p>I've heard both of these Pali terms translated to the English term "effort".</p>

<p>1: sammā-vāyāma: the 6th item in the 8-fold path.<br>
2: virya: the 2nd of the 5 faculties/powers/Indrias.</p>

<p>If 2 terms are used instead of 1, they probably represent slightly different concepts but the similarity and difference between these 2 is unclear to me.</p>

<p>My best guess from my fuzzy understanding is ...</p>

<p>Gil Fronsdal has identified virya as being a kind of "heroic effort".
It's part of the 5 Indrias and Indra was the god that ruled the other gods so perhaps this refers to an heroic effort to rule over the hindrances?</p>

<p>sammā-vāyāma is associated with the 4 right exertions.
As such it seems to be about moving away from unwholesome states and towards wholesome states.</p>

<p>The 2 terms seem very similar.
The only difference I can detect is that the "heroic" modifier associated with virya suggests a stronger emphasis on courage and/or aggression.</p>

<p>Is this correct?</p>
 16297: <p>samma padhana (right exertion from 37 bodhi pakkhiya), viriya-indriya, viriya sambojjhanga (of 7 awakening factors), samma vayamo (right effort of noble eightfold path) are equivalent. The slightly different official definition for each term, is meant to highlight a particular aspect of right effort.</p>

<p>You'll notice in the right effort definition (SN 45.8), all of those words are found in the formula (vayamati/vayamo, viriya, padahati/padhana). </p>

<p>Another word that frequently occurs in the suttas, such as in the satipatthana formula, 'ātāpi' (ardency), is a code word that also means the same right effort formula (see AN 4.14 verse at end)
<a href="http://lucid24.org/an/an04/an04-0014/index.html" rel="nofollow noreferrer">http://lucid24.org/an/an04/an04-0014/index.html</a></p>
 8157: <p>Their contextual use in the suttas is the same, as follows:</p>

<blockquote>
  <p>And what is right <strong>effort</strong>? Katamo ca, bhikkhave, sammā<strong>vāyāmo</strong>?</p>
  
  <p>It’s when a mendicant generates enthusiasm, tries, makes an effort,
  exerts the mind, and strives so that bad, unskillful qualities don’t
  arise. Idha, bhikkhave, bhikkhu anuppannānaṃ pāpakānaṃ akusalānaṃ
  dhammānaṃ anuppādāya chandaṃ janeti <strong>vāyamati vīriyaṃ</strong> ārabhati cittaṃ
  paggaṇhāti padahati,</p>
  
  <p>SN 45.8</p>
  
  <hr>
  
  <p>And what is the faculty of <strong>energy</strong>? Katamañca, bhikkhave,
  <strong>vīriy</strong>indriyaṃ?</p>
  
  <p>It’s when a mendicant lives with energy roused up for giving up
  unskillful qualities and embracing skillful qualities. They’re strong,
  staunchly vigorous, not slacking off when it comes to developing
  skillful qualities. Idha, bhikkhave, ariyasāvako āraddhavīriyo
  viharati akusalānaṃ dhammānaṃ pahānāya, kusalānaṃ dhammānaṃ
  upasampadāya, thāmavā daḷhaparakkamo anikkhittadhuro kusalesu dhammesu.</p>
  
  <p>They generate enthusiasm, try, make an effort, exert the mind, and
  strive so that bad, unskillful qualities don’t arise. So anuppannānaṃ
  pāpakānaṃ akusalānaṃ dhammānaṃ anuppādāya chandaṃ janeti <strong>vāyamati
  vīriyaṃ</strong> ārabhati cittaṃ paggaṇhāti padahati</p>
  
  <p>SN 48.10</p>
</blockquote>

<p>The word 'vāyāma' is derived from 'vi + ā + yam' where 'yam' or 'yāma' appears to mean '<em>restraint</em>', '<em>don't do</em>', '<em>reining in</em>' or '<em>control</em>'. One fluent in Pali will need to explain how 'vi + ā' modify 'yāma'.  </p>

<p>The word 'viriya' I guess is derived from 'vīra + ya' and is said to literally mean '<a href="https://suttacentral.net/define/viriya" rel="nofollow noreferrer">state of a strong man</a>'. '<a href="http://spokensanskrit.org/index.php?tran_input=vIra&amp;direct=se&amp;script=hk&amp;link=yes&amp;mode=3" rel="nofollow noreferrer">Vīra</a>' means 'strong', 'brave' or 'heroic' thus 'ya' must mean 'state'. </p>

<p>Therefore, merely guessing, 'viriya' appears to be a 'thing', namely, 'energy'; where as 'vāyāma' appears related to acting or related to a verb, i.e., possibly a '<em>verbal noun</em>'. In other words, in the Pali above, there is the phrase '<em>vāyamati vīriyaṃ</em>'. Here, 'vāyamati' (due to ending in 'ati') is a verb; where as 'vīriyaṃ' is a noun. Thus, the phrase '<em>vāyamati vīriyaṃ</em>' appears to mean: '<em>to exercise energy</em>' or '<em>to exert energy</em>'.  </p>

<p>In summary, 'vayama' appears related to the action of acting; where as 'viriya' appears related to the quality of acting. This said, I could be wrong, here, because I am merely guessing. </p>
 13709: <p>Sometimes a look at opposite terms can help.</p>

<p>For <em>avāyāmaṃ</em> we have weakly directed effort:</p>

<blockquote>
  <p><a href="https://suttacentral.net/sn11.1/en/sujato#sn11.1:3.3" rel="nofollow noreferrer">SN11.1:3.3</a>: without working for it or trying hard—</p>
</blockquote>

<p>For <em>avīriyā</em> we have apathetic lethargy:</p>

<blockquote>
  <p><a href="https://suttacentral.net/mn60/en/sujato#mn60:21.7" rel="nofollow noreferrer">MN60:21.7</a>: All sentient beings, all living creatures, all beings, all souls lack control, power, and energy. Molded by destiny, circumstance, and nature, they experience pleasure and pain in the six classes of rebirth.’</p>
</blockquote>
