Are both Pali-words synonyms or is there a slight difference between 'patinissagga' and 'vossagga'?
While not always, paṭinissagga is often used for more lofty situations, such as connected to Nibbana (in SN 56.11; AN 3.32 & MN 118).
Vossagga appears always used in less lofty situations and appears more 'personal'.
enclitic from tumha
to you; of you; by you
Each use of each word in the suttas should be examined; as for the etymology of each word. A post on the topic is here.
MN 118 contains both words. 'Vossagga' is found describing the maturation of the qualities each factor of enlightenment relies upon. Therefore, 'vossagga' appears used with path factors Anapanasati relies on.
'Paṭinissagga' is used to describe the end of the path of Anapanasati. Therefore, 'paṭinissagga' appears more lofty than 'vossagga'.
Start with 'vossagga' and end with 'paṭinissagga'.
It’s when a mendicant develops the awakening factors of mindfulness, investigation of principles, energy, rapture, tranquility, immersion, and equanimity, which rely on seclusion, fading awa, and cessation that ripen as letting go.
Idha, bhikkhave, bhikkhu satisambojjhaṅgaṃ bhāveti vivekanissitaṃ virāganissitaṃ nirodhanissitaṃ vossaggapariṇāmiṃ. Dhammavicayasambojjhaṅgaṃ bhāveti … pe … vīriyasambojjhaṅgaṃ bhāveti … pītisambojjhaṅgaṃ bhāveti … passaddhisambojjhaṅgaṃ bhāveti … samādhisambojjhaṅgaṃ bhāveti … upekkhāsambojjhaṅgaṃ bhāveti vivekanissitaṃ virāganissitaṃ nirodhanissitaṃ vossaggapariṇāmiṃ.
They practice breathing in observing impermanence. They practice breathing out observing impermanence.
‘Aniccānupassī assasissāmī’ti sikkhati, ‘aniccānupassī passasissāmī’ti sikkhati;
They practice breathing in observing fading away. They practice breathing out observing fading away.
‘virāgānupassī assasissāmī’ti sikkhati, ‘virāgānupassī passasissāmī’ti sikkhati;
They practice breathing in observing cessation. They practice breathing out observing cessation.
‘nirodhānupassī assasissāmī’ti sikkhati, ‘nirodhānupassī passasissāmī’ti sikkhati;
They practice breathing in observing letting go. They practice breathing out observing letting go.
‘paṭinissaggānupassī assasissāmī’ti sikkhati, ‘paṭinissaggānupassī passasissāmī’ti sikkhati.
In conclusion, 'vossagga' may possibly mean when the 'self' or 'will' lets go by employing mindfulness to bring to mind right view. Where as 'paṭinissaggā' may possibly mean when the mind itself lets go due to direct seeing or vipassana.
It seems to me, 'patinissagga' means gradual and progressive letting go (or giving up), while 'vossagga' simply means letting go, without emphasizing the progression.
Pati or prati looks like the same prefix as in 'pratipada' and 'pratityasamutpada'. In my research, prati implies that something happens in multiple stages as opposed to all at once.
So I suppose 'patinissagga' tells us to methodically let go, first of more obvious hang-ups and then of progressively more and more subtle, I think.
Paṭinissagga : giving up, forsaking; rejection, renunciation
Vossagga : relinquishing, relaxation; handing over, donation, gift
sati-Vossagga : relaxation of attention, inattention, indifference
Vossajjati : to give up, relinquish; to hand over, resign
The difference, if any, appears to be in a greater emphasis of vossaga on the mental or personal side of the issue of letting go.