user-1: The Second Noble Truth identifies three aspects of craving, one of them being craving for non-being.
How does the desire for cessation, to attain final Nibbāna, never to be reborn, differ from the desire for non-existence? 

user254: I think that, according to Ananda in SN 51.15, the holy life is "give up or abandon desire" -- perhaps also (my paraphrase) "aiming towards [[being in] a state of] non-craving".
Having reached that state (of non-craving) then the desire is calmed.
Perhaps it's obvious that's not the same as craving for annihilation.

Dhammadhatu's answer mentioned chanda iddhipada which is analyzed e.g. in SN 51.20.
In both these suttas, 51.15 and 51.20 (and actually all of the SN 51.xx suttas describe the Iddhipada), Ven Sujato translates chanda as "enthusiasm" rather than "desire".

user8157: Vibhava tanha (craving not-to-be) is a type of craving. 
Cessation of being (bhava nirodha) is the cessation of craving (tanha nirodha). 
The "desire for cessation" called 'chanda iddhipada' is not a type of craving (tanha). 
Also, bhava nirodha is not "never to be reborn". "Bhava" is "egoism". "Bhava nirodha" is the cessation of egoism. 
If mind believes believes in "ego" or "self", now can it ever stop being "reborn"? 
"Jati" ("birth") itself means "egoism'. "Jati nirodha" happens when egoism stops. 
The only way to reach Nibbana is stopping egoism. 

-1: <p>The Second Noble Truth identifies three aspects of craving, one of them being craving for non-being.</p>

<p>How does the desire for cessation, to attain final Nibbāna, never to be reborn, differ from the desire for non-existence? </p>
 254: <p>I think that, according to Ananda in <a href="https://suttacentral.net/sn51.15/en/sujato" rel="nofollow noreferrer">SN 51.15</a>, the holy life is "give up or abandon desire" -- perhaps also (my paraphrase) "aiming towards [[being in] a state of] non-craving".</p>

<p>Having reached that state (of non-craving) then the desire is calmed.</p>

<p>Perhaps it's obvious that's not the same as craving for annihilation.</p>

<hr>

<p>Dhammadhatu's answer mentioned <em>chanda iddhipada</em> which is analyzed e.g. in <a href="https://suttacentral.net/sn51.20/en/sujato" rel="nofollow noreferrer">SN 51.20</a>.</p>

<p>In both these suttas, 51.15 and 51.20 (and actually all of the <a href="https://suttacentral.net/sn51" rel="nofollow noreferrer">SN 51.xx</a> suttas describe the <a href="https://en.wikipedia.org/wiki/Iddhipada" rel="nofollow noreferrer">Iddhipada</a>), Ven Sujato translates <em><a href="https://suttacentral.net/define/chanda" rel="nofollow noreferrer">chanda</a></em> as "enthusiasm" rather than "desire".</p>
 8157: <p>Vibhava tanha (craving not-to-be) is a type of craving. </p>

<p>Cessation of being (bhava nirodha) is the cessation of craving (tanha nirodha). </p>

<p>The "desire for cessation" called '<em>chanda iddhipada</em>' is not a type of craving (tanha). </p>

<p>Also, bhava nirodha is not "<em>never to be reborn</em>". "Bhava" is "egoism". "Bhava nirodha" is the cessation of egoism. </p>

<p>If mind believes believes in "ego" or "self", now can it ever stop being "reborn"? </p>

<p>"Jati" ("birth") itself means "egoism'. "Jati nirodha" happens when egoism stops. </p>

<p>The only way to reach Nibbana is stopping egoism. </p>
