Well, most of these are just verbal variations, i.e. different forms of the same word. As for the distinct terms, we have:
abhinibbatti = rebirth (pretty much only used in this sense)
opapātika = spontaneously reborn, i.e. like the gods (this is technically just a verbal derivation from uppatti = uppajjati, but is used in this specific sense.)
paccājāyati = paṭi + ā + jāyati i.e. literally “re + born”. (Sometimes people assert that there is no word that means “rebirth” in pali. Apart from being a nonsensical way of thinking about language, you can direct them this way, for paccājāyati is a close a direct linguistic equivalent of “rebirth” as you could hope for.)
upapajjati = “to be reborn” the more common verb used in the same sense as paccājāyati.
uppajjati = “arises”, used in a general sense, in some cases overlapping with that of rebirth; consider for example the common phrase Tathāgato loke uppajjati (“A Realized One arises in the world …”) It doesn’t quite mean that he is reborn, but it’s not all that different in meaning either.
The standard definition of rebirth in the suttas includes the synonyms jāti sañjāti okkanti abhinibbatti. Of these:
jāti = usually translated “birth”, but in fact generally used in the sense of “rebirth”. See next.
sañjāti = rebirth in the specific sense of “conception”, as opposed to vijāti which means “parturition” i.e. “birth” in the usual sense. (Google defines birth as “the emergence of a baby or other young from the body of its mother; the start of life as a physically separate being.”)
okkanti = “conception” in the sense of the “descent” (too literal!) or arrival of the “spirit” (in animist thinking) or “consciousness” (in Buddhism).
In addition to these, we also have bhava and its various forms (punabbhava, punabhavabhinibbatti, etc.). This has the more general sense of “life, existence, state of rebirth”, but used loosely it often has the sense of “rebirth”, as in, say bhavanetti, “attachment to existence”, i.e. “attachment to future lives”, i.e. “attachment to being reborn”.
Thank you for your comprehensive answers Ajahn Sujato.
What about the word “labhati”, where SN 56.48 states: 'Evaṃ adhiccamidaṃ, bhikkhave, yaṃ manussattaṃ labhati: So too, bhikkhus, it is by chance that one obtains the human state".
Is ‘labhati’ related to ‘paṭilābho’ found’ in the definition of ‘jati’ (‘birth’) from SN 12.2, namely, ‘khandhānaṃ pātubhāvo āyatanānaṃ paṭilābho’? If so, how does the prefix ‘paṭi’ apply?
Yes, it’s the same word. In this case the prefix pati- doesn’t mean very much. You could translate it as “re” I suppose: “the regaining of the sense fields”. But this is probably overly literal.
Again, it’s a general term that just happens to be used here in the context of rebirth, rather than a term that specifically means rebirth as such.
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