There are variant "present" words' meanings in tipitaka and commentaries because of variant sutta contexts such as ability of listener, etc.
Commentaries collected "present" words in tipitaka as 3 periods: present by rebirth period, present by doing period, and present by citta&rūpa arising period. Another "present" word that focus on arising khandha, now.
present by birth period (addhāna-paccupanna)
The kammaṭṭhāna teacher, such as buddha, will teach this meaning to the beginner practitioner who has gotten jhāna or uggatitaññū/diṭṭhicarita-vipacitaññū. So this meaning always use in suttanta-pitaka especially paṭiccasamuppāda. So in abhidhamma-pitaka, vibhaṅga that was memorized by sariputta-mahāsāvaka then retaught in his literal, wrote that paṭiccasamuppāda by rebirth, is suttanta-method. And in paṭisambhidāmagga, that author by sāriputta-mahāsāvaka, wrote that viññāṇa-paṭiccasamuppāda is rebirth (paṭisaṇdhi). Also bhaddekarattasutta.
present by doing period (santati-paccupanna)
The kammaṭṭhāna teacher, such as buddha, will teach this meaning to a fool who can not get high level vipassanā (udayabbayañāṇa) or neyya/taṇhācarita-vipacitaññū. For the example in mahāsatipaṭṭhānasutta "sāmissaṃ vā sukkhaṃ vedanaṃ vediyamāno sāmissaṃ sukkhaṃ vedanaṃ vediyāmīti pajānāti". Or in commentary such as arūpadhammānaṃ upaṭṭhānākārakathā
and indriyatikkhakāraṇanavakakathā of visuddhimagga.
***Doing period is period between after come from the hotter temperature place then sit in the colder place, between the temperature changing is present doing period. Another same vīthi's javanāni are present doing period.
present by citta&rūpa period (khaṇa-paccupanna, paccuppannā dhammā)
***Khaṇa is the smallest period in the universe. It is just arising part+lving part+vanishing part (3 anukhaṇa) of citta&rūpa. There are more than trillion khanā while just snapping fingers. Every suffering truth that have own causes to make it's arising, has their own khaṇa period. So 11 group khandha have their own present arising: past khandha arising, future khandha arising, present khandha arising, self khandha arising, others khandha arising, not smooth khandha arising, smooth khandha arising, good khandha arising, and bad khandha khandha arising. So past and future khandha are reality, that is the object of vipassanā meditation, too.
Arising Present khandha As the Object Of Vipassanā Meditation
The kammaṭṭhāna teacher, such as buddha, will teach this meaning to the advance practitioner who can clearly comprehend paṭiccasamuppāda. Because practitioner who already understand paṭiccasamuppāda, has already seen anicca/dukkha/anatta-lakkhaṇa of the whole khandha (11 group khandha: past, future, present, self, others, not smooth, smooth, good, and bad khandha). He already has auto clearly comprehended in them, so when he is sitting to do vipassanā meditate, without the other jobs, his object should be the present himself that comprehending another object. Present himself, arising khandha khaṇa, is the closest khandha to
be attached by taṇhā/diṭṭhi/māna. The mahāsatipaṭṭhānasutta's commentary very focus in this meaning, because kuru people are uggaṭitaññū.
P.S. It is very very deep,very hard to explain. Please see every reference to understand "present".