Below are some of the key terms. You might find more if you check out the entry for Gotama Buddha in the Dictionary of Proper Names and chase up the references.
Three divisions of the Buddha’s post-awakening life
paṭhamabodhi
majjhimabodhi
pacchimabodhi
(Several Vinaya ṭīkās report a difference of opinion over how the years of these periods are to be counted. One opinion was that they were three periods of fifteen years each. Another was that the paṭhamabodhi was twenty years, the pacchimabodhi just the months leading up to the Parinibbāna, and everything in between was the majjhimabodhi. In ṭīkās (occasionally) and in SE Asian Buddha biographies (very frequently) one also meets with paṭhamabodhikāla, majjhimabodhikāla, and pacchimabodhikāla).
Ten divisions of the Buddha’s whole life
gabbhokkanti-samaya
jāti-samaya
saṃvega-samaya
abhinikkhamana-samaya
dukkarakārika-samaya
māravijaya-samaya
abhisambodhi-samaya
diṭṭhadhammasukhavihāra-samaya
desanā-samaya
parinibbāna-samaya
Where the Buddha spent his forty-five rains residences
Kadā desito ti bhagavā hi paṭhamabodhiyaṃ vīsativassāni anibaddhavāso hutvā yattha yattha phāsukaṃ hoti, tattha tattheva gantvā vasi. Kathaṃ?
Paṭhamaṃ vassaṃ isipatane dhammacakkaṃ pavattetvā aṭṭhārasa brahmakoṭiyo amatapānaṃ pāyetvā bārāṇasiṃ upanissāya isipatane migadāye vasi.
Dutiyaṃ vassaṃ rājagahaṃ upanissāya veḷuvane mahāvihāre.
Tatiyacatutthāni pi tattheva.
Pañcamaṃ vesāliṃ upanissāya mahāvane kūṭāgārasālāyaṃ.
Chaṭṭhaṃ makulapabbate.
Sattamaṃ tāvatiṃsabhavane.
Aṭṭhamaṃ bhaggesu saṃsumāragiriṃ upanissāya bhesakaḷāvane.
Navamaṃ kosambiyaṃ.
Dasamaṃ pālileyyakavanasaṇḍe.
Ekādasamaṃ nāḷāyaṃ brāhmaṇagāme.
Dvādasamaṃ verañjāyaṃ.
Terasamaṃ cāliyapabbate.
Cuddasamaṃ jetavanamahāvihāre.
Pañcadasamaṃ kapilavatthumahānagare.
Soḷasamaṃ āḷavakaṃ dametvā caturāsītipāṇasahassāni amatapānaṃ pāyetvā āḷaviyaṃ.
Sattarasamaṃ rājagaheyeva.
Aṭṭhārasamaṃ cāliyapabbateyeva.
Tathā, ekūnavīsatimaṃ vīsatimaṃ pana vassaṃ rājagaheyeva vasi.
Tena vuttaṃ: “bhagavā hi paṭhamabodhiyaṃ vīsativassāni anibaddhavāso hutvā yattha yattha phāsukaṃ hoti, tattha tattheva gantvā vasī” ti. Tato paṭṭhāya pana sāvatthiṃyeva upanissāya jetavanamahāvihāre ca pubbārāme ca dhuvaparibhogavasena vasi.
(Bv-a. 3-4)
Other terms
ordinal number in the masc. sg. loc. case + saṃvacchare
abhisambodhiṃ patvā/patto/pāpuṇitvā: “after attaining supreme awakening…”
abhisambodhito…: “from [the time of] supreme awakening…”
abhisambodhito paṭṭhāya…: “reckoning from [the time of] supreme awakening…”