user2495: Is there a difference between abhava and vibhava? Or are those words synonyms?
When they are not synonyms, what is their exact meaning.

user7548: I recently stumbled upon an interesting explanation of vibhavataṇhā in the german translation of the Majjhima Nikāya by Mettiko Bhikkhu. I tried to translate this explanation as good as I could into english. The following is from page 25 (3rd edition, 2014):

Bhavataṇhā generally is craving for being, or in a more precise case the craving for being in the current, present situation.
Vibhavataṇhā often is misunderstood as craving for non-existence. That is linguistcally wrong, because the prefix "vi-" does not mean "not", but it means "different than, dis-, apart-, parallel to". (A-bhava, not-becoming/non-existence only occurs very rarely in the texts and in different contexts.) Furthermore would "craving for non-existence" mean, that the Buddha teaches a fundamental category, which only applies to specific people at a specific times -- a contradiction in terms, which is not consistent with the spirit/tenor of the Suttas.
From an existential point of view it's also impossible to imagine "non-existence/being" or to wish it. Even a potential suicide does not wish for 'nothing', but rather for 'something else'.
Vibhavataṇhā is a potential/possible existence/state of being, which we use to isolate and define our present existence/state of being, regardless of whether these possibilities are going to become true or not. Just as it only makes sense to speak about the color red when there are things that are not red, our existence becomes established by the possibilities that we have within it (or around it). An example: How often do we speak while eating about different food or things we ate in the past or might eat in the future, even if the present meal is 100% satisfying?
That's why I'll translate Vibhavataṇhā as "Craving for potential existence", the craving for a background for the own existence. The philosophical fun question "Life is strange ... compared to what?" therefore is not far fetched.
This kind of craving is one of the three forms of the source of a relative, conditioned personality (sakkāya) as it is described in the teachings of the Buddha (for example in M44). Follower of other teachings that don't base on conditions, postulate the existence of an absolute, permanent, independent self. In their language, referring to an absolute self, the sense of "being-different-than" (Vibhavataṇhā) can of course only mean annihilation and in these cases is also translated as such, as well as when the Buddha talks about the standpoint of those teachings (i.e. M102).

I might adjust/refine the translation, if there is some feedback. But for now, I hope a sloppy (sometimes word by word) translation is enough.
In summary, what this section says is that Vibha within the Buddha's teaching can mean two things:

non-existence, if a different philosophy or teaching is addressed, which states a permanent self.
Craving to be different, become somebody else (Which I think is what is meant by "craving for potential existence").


user254: Let's assume that bhava means "existence".
I think that the a prefix means "not" (it appears in a lot of Buddhist words, like anatta and so on).
I think that the vi prefix might mean "the reverse of" (see e.g. the dictionary definition quoted here).
So my guess is that abhava means "non-existence", whereas vibhava means "destruction".
The phrase vibhavataṇhā is used in the definition of the second noble truth in SN 56.11, so you can read various translations of vibhava in the various translations of that sutta, for example:


craving for extermination (of what is not liked)
craving for non-being
craving for non-existence (self-annihilation)
craving for non-becoming
craving for non-existence [for extinction].


The first translation of SN 56.11 that I read translated bhavataṇhā and vibhavataṇhā as "the craving to live and even the craving to die", so that's the way I remember it.
In summary, maybe they mean the same thing (i.e. "non-existence"); but if they aren't synonyms, then one simply means "non-existence" and the other implies a "transition from existence to non-existence" for example "annihilation, destruction, extinction, death".

user8157: 'Vibhava' is a form of 'becoming' or 'self-view', namely, the idea "I do not exist" or "I do not want to exist" or "I will cease to exist". Since the idea of 'I' ('atta') or "a being/person" ('satta') still remains, 'vibhava' is a type of becoming (bhava). This is described in the following suttas: 

Tayidaṃ, bhikkhave, tathāgato abhijānāti. Ye kho te bhonto samaṇabrāhmaṇā sato sattassa ucchedaṃ vināsaṃ vibhavaṃ paññapenti
  te sakkāyabhayā sakkā­ya­pari­je­gucchā sakkāyaññeva
  anupa­ri­dhāvanti anu­pari­vattanti. Seyyathāpi nāma sā gaddulabaddho
  daḷhe thambhe vā khile vā upanibaddho, tameva thambhaṃ vā khilaṃ vā
  anuparidhāvati anuparivattatianuparivattati evamevime bhonto
  samaṇabrāhmaṇā sakkāyabhayā sakkā­ya­pari­je­gucchā sakkāyaññeva
  anupa­ri­dhāvanti anu­pari­vattanti.
Those recluses that describe the annihilation, destruction & extermination (vibhavaṃ; non-existence) of an existing being (sattassa);
  through fear & disgust with identity (sakkāya), keep running &
  circling around that same identity; just as a dog bound by a leash to
  a post keeps running & circling around that same post....
MN 102.12

Kathañca, bhikkhave, atidhāvanti eke? Bhaveneva kho paneke aṭṭīyamānā harāyamānā jigucchamānā vibhavaṃ abhinandanti—yato kira, bho, ayaṃ
  attā kāyassa bhedā paraṃ maraṇā ucchijjati vinassati na hoti paraṃ
  maraṇā; etaṃ santaṃ etaṃ paṇītaṃ etaṃ yāthāvanti. Evaṃ kho, bhikkhave,
  atidhāvanti eke.
How, bhikkhus, do some overreach? Now some are troubled, ashamed and disgusted by this very same being and they rejoice in (the idea of)
  non-being, asserting: ‘In as much as this self, good sirs, when the
  body perishes at death, is annihilated and destroyed and does not
  exist after death—this is peaceful, this is excellent, this is
  reality!’ Thus, bhikkhus, do some overreach.
Iti 44


As for 'abhava', I do not currently know what it means in Pali Buddhism. 
'Abhava' appears to not have the same meaning as 'abhavissā', which seems to mean: 'if was' or 'would have been', as found in the 2nd sermon: 

Rūpañca hidaṃ, bhikkhave, attā abhavissa, nayidaṃ rūpaṃ ābādhāya saṃvatteyya
For if, bhikkhus, form were self, this form would not lead to affliction...


'Vibhava' is not a synonym for Nibbana or the Unconditioned. MN 140 states:

So nevaneva taṃ abhisaṅkharoti, na abhisañ­ceta­yati bhavāya vā vibhavāya vā. So anabhi­saṅ­kha­ronto anabhi­sañ­ceta­yanto bhavāya vā
  vibhavāya vā na kiñci loke upādiyati, anupādiyaṃ na paritassati,
  aparitassaṃ paccattaṃyeva parinibbāyati
He does not form any condition or generate any volition tending towards either being or non-being. Since he does not form any
  condition or generate any volition tending towards either being or
  non-being, he does not cling to anything in this world. When he does
  not cling, he is not agitated. When he is not agitated, he personally
  attains Nibbāna.



In Hinduism, 'abhava' appears to refer to a primordial unconditioned state, namely, unmanifest level from where the concrete bhava arises or emerges.
'Abhava' here, in Hinduism, is not a synonymous with 'vibhava' in Buddhism because, in Buddhism, 'bhava' ('becoming') must occur before 'vibhava' can occur. 
The idea of 'I' is 'bhava'. The idea of "I" must exist before the idea of "I do not want to exist" can occur. For example, the idea of "I", "me" or "self" must occur before the wish to commit suicide. 

2495: <p>Is there a difference between <em>abhava</em> and <em>vibhava</em>? Or are those words synonyms?</p>

<p>When they are not synonyms, what is their exact meaning.</p>
 7548: <p>I recently stumbled upon an interesting explanation of <em>vibhavataṇhā</em> in the german translation of the Majjhima Nikāya by Mettiko Bhikkhu. I tried to translate this explanation as good as I could into english. The following is from page 25 (3rd edition, 2014):</p>
<blockquote>
<p><em>Bhavataṇhā</em> generally is craving for being, or in a more precise case the craving for being in the current, present situation.</p>
<p><em>Vibhavataṇhā</em> often is misunderstood as craving for non-existence. That is linguistcally wrong, because the prefix <em>&quot;vi-&quot;</em> does not mean <em>&quot;not&quot;</em>, but it means <em>&quot;different than, dis-, apart-, parallel to&quot;</em>. (<em>A-bhava</em>, not-becoming/non-existence only occurs very rarely in the texts and in different contexts.) Furthermore would &quot;craving for non-existence&quot; mean, that the Buddha teaches a fundamental category, which only applies to specific people at a specific times -- a contradiction in terms, which is not consistent with the spirit/tenor of the Suttas.</p>
<p>From an existential point of view it's also impossible to imagine &quot;non-existence/being&quot; or to wish it. Even a potential suicide does not wish for 'nothing', but rather for 'something else'.</p>
<p><em>Vibhavataṇhā</em> is a potential/possible existence/state of being, which we use to isolate and define our present existence/state of being, regardless of whether these possibilities are going to become true or not. Just as it only makes sense to speak about the color red when there are things that are <em>not</em> red, our existence becomes established by the possibilities that we have within it (or around it). An example: How often do we speak while eating about different food or things we ate in the past or might eat in the future, even if the present meal is 100% satisfying?</p>
<p>That's why I'll translate <em>Vibhavataṇhā</em> as &quot;Craving for potential existence&quot;, the craving for a background for the own existence. The philosophical fun question &quot;Life is strange ... compared to what?&quot; therefore is not far fetched.</p>
<p>This kind of craving is one of the three forms of the source of a relative, conditioned personality (sakkāya) as it is described in the teachings of the Buddha (for example in M44). Follower of other teachings that don't base on conditions, postulate the existence of an absolute, permanent, independent self. In their language, referring to an absolute self, the sense of &quot;being-different-than&quot; (<em>Vibhavataṇhā</em>) can of course only mean annihilation and in these cases is also translated as such, as well as when the Buddha talks about the standpoint of those teachings (i.e. M102).</p>
</blockquote>
<p>I might adjust/refine the translation, if there is some feedback. But for now, I hope a sloppy (sometimes word by word) translation is enough.</p>
<p>In summary, what this section says is that <em>Vibha</em> within the Buddha's teaching can mean two things:</p>
<ul>
<li>non-existence, if a different philosophy or teaching is addressed, which states a permanent self.</li>
<li>Craving to be different, become somebody else (Which I think is what is meant by &quot;craving for potential existence&quot;).</li>
</ul>
 254: <p>Let's assume that <em>bhava</em> means "existence".</p>

<p>I think that the <em>a</em> prefix means "not" (it appears in a lot of Buddhist words, like anatta and so on).</p>

<p>I think that the <em>vi</em> prefix might mean "the reverse of" (see e.g. the dictionary definition <a href="https://buddhism.stackexchange.com/a/19958/254">quoted here</a>).</p>

<p>So my guess is that <em>abhava</em> means "non-existence", whereas <em>vibhava</em> means "destruction".</p>

<p>The phrase <em>vibhavataṇhā</em> is used in the definition of the second noble truth in SN 56.11, so you can read various translations of <em>vibhava</em> in the various translations of that sutta, for example:</p>

<blockquote>
  <ul>
  <li>craving for extermination (of what is not liked)</li>
  <li>craving for non-being</li>
  <li>craving for non-existence (self-annihilation)</li>
  <li>craving for non-becoming</li>
  <li>craving for non-existence [for extinction].</li>
  </ul>
</blockquote>

<p>The first translation of SN 56.11 that I read translated <em>bhavataṇhā</em> and <em>vibhavataṇhā</em> as "the craving to live and even the craving to die", so that's the way I remember it.</p>

<p>In summary, maybe they mean the same thing (i.e. "non-existence"); but if they aren't synonyms, then one simply means "non-existence" and the other implies a "transition from existence to non-existence" for example "annihilation, destruction, extinction, death".</p>
 8157: <p>'<strong>Vibhava</strong>' is a form of 'becoming' or 'self-view', namely, the idea "<em>I do not exist</em>" or "<em>I do not want to exist</em>" or "<em>I will cease to exist</em>". Since the idea of 'I' ('<em>atta</em>') or "a being/person" ('<em>satta</em>') still remains, 'vibhava' is a type of becoming (bhava). This is described in the following suttas: </p>

<blockquote>
  <p><em>Tayidaṃ, bhikkhave, tathāgato abhijānāti. Ye kho te bhonto samaṇabrāhmaṇā sato <strong>sattassa</strong> ucchedaṃ vināsaṃ <strong>vibhavaṃ</strong> paññapenti
  te <strong>sakkāya</strong>bhayā sakkā­ya­pari­je­gucchā <strong>sakkāyaññeva</strong>
  anupa­ri­dhāvanti anu­pari­vattanti. Seyyathāpi nāma sā gaddulabaddho
  daḷhe thambhe vā khile vā upanibaddho, tameva thambhaṃ vā khilaṃ vā
  anuparidhāvati anuparivattatianuparivattati evamevime bhonto
  samaṇabrāhmaṇā sakkāyabhayā sakkā­ya­pari­je­gucchā sakkāyaññeva
  anupa­ri­dhāvanti anu­pari­vattanti.</em></p>
  
  <p><em>Those recluses that describe the annihilation, destruction &amp; <strong>extermination</strong> (vibhavaṃ; non-existence) of an <strong>existing being</strong> (sattassa);
  through fear &amp; disgust with <strong>identity</strong> (sakkāya), keep running &amp;
  circling around that <strong>same identity</strong>; just as a dog bound by a leash to
  a post keeps running &amp; circling around that same post....</em></p>
  
  <p><em>MN 102.12</em></p>
  
  <hr>
  
  <p><em>Kathañca, bhikkhave, atidhāvanti eke? <strong>Bhaveneva</strong> kho paneke aṭṭīyamānā harāyamānā jigucchamānā <strong>vibhavaṃ</strong> abhinandanti—yato kira, bho, ayaṃ
  <strong>attā</strong> kāyassa bhedā paraṃ maraṇā ucchijjati vinassati na hoti paraṃ
  maraṇā; etaṃ santaṃ etaṃ paṇītaṃ etaṃ yāthāvanti. Evaṃ kho, bhikkhave,
  atidhāvanti eke.</em></p>
  
  <p><em>How, bhikkhus, do some overreach? Now some are troubled, ashamed and disgusted by <strong>this very same</strong> <strong>being</strong> and they rejoice in (the idea of)
  <strong>non-being</strong>, asserting: ‘In as much as this <strong>self</strong>, good sirs, when the
  body perishes at death, is annihilated and destroyed and does not
  exist after death—this is peaceful, this is excellent, this is
  reality!’ Thus, bhikkhus, do some overreach.</em></p>
  
  <p><em>Iti 44</em></p>
  
  <hr>
</blockquote>

<p>As for '<strong>abhava</strong>', I do not currently know what it means in Pali Buddhism. </p>

<p>'Abhava' appears to not have the same meaning as '<strong>abhavissā</strong>', which seems to mean: 'if was' or 'would have been', as found in the 2nd sermon: </p>

<blockquote>
  <p><em>Rūpañca hidaṃ, bhikkhave, attā <strong>abhavissa</strong>, nayidaṃ rūpaṃ ābādhāya saṃvatteyya</em></p>
  
  <p><em>For <strong>if</strong>, bhikkhus, form <strong>were</strong> self, this form would not lead to affliction...</em></p>
  
  <hr>
</blockquote>

<p>'<strong>Vibhava</strong>' is not a synonym for Nibbana or the Unconditioned. MN 140 states:</p>

<blockquote>
  <p><em>So nevaneva taṃ abhisaṅkharoti, na abhisañ­ceta­yati bhavāya vā <strong>vibhavā</strong>ya vā. So anabhi­saṅ­kha­ronto anabhi­sañ­ceta­yanto bhavāya vā
  <strong>vibhavā</strong>ya vā na kiñci loke upādiyati, anupādiyaṃ na paritassati,
  aparitassaṃ paccattaṃyeva parinibbāyati</em></p>
  
  <p><em>He does not form any condition or generate any volition tending towards either being or non-being. Since he does not form any
  condition or generate any volition tending towards either being or
  non-being, he does not cling to anything in this world. When he does
  not cling, he is not agitated. When he is not agitated, he personally
  attains Nibbāna.</em></p>
</blockquote>

<hr>

<hr>

<p>In Hinduism, '<a href="https://en.wikipedia.org/wiki/Abhava" rel="nofollow noreferrer"><strong>abhava</strong></a>' appears to refer to a primordial unconditioned state, namely, unmanifest level from where the concrete bhava arises or emerges.</p>

<p>'Abhava' here, in Hinduism, is not a synonymous with 'vibhava' in Buddhism because, in Buddhism, 'bhava' ('becoming') must occur before 'vibhava' can occur. </p>

<p>The idea of 'I' is 'bhava'. The idea of "I" must exist before the idea of "<em>I do not want to exist</em>" can occur. For example, the idea of "I", "me" or "self" must occur before the wish to commit suicide. </p>
