In Mahayana Buddhism, what is the difference between abiding nirvana and non-abiding nirvana?
Are there official Sanskrit terms for "abiding nirvana" and "non-abiding nirvana"? What are they?
When a Buddha has achieved non-abiding nirvana, "his enlightened activities are uninterrupted". What does this mean?
This question is based on this answer:
A Hinayana arhat abandoned afflictive obscurations by way of realizing emptiness, but has not abandoned knowledge obscuration. He has achieved abiding nirvana. Therefore, although they are free from the conception of true existence, and from true suffering, they are not free from the imprints of ignorance (i.e. knowledge obscurations). We say that it is like removing garlic from a container: the smell will still be there. So, because they still have the imprints of ignorance, (1) they are not free from the appearance of true existence, and (2) they are reborn with a mental body, due to the imprints of ignorance (in our case, we are reborn to due karma and afflictions).
A bodhisattva is a person who generated effortless bodhicitta (the wish to achieve enlightenment for the sake of all sentient beings). Since effortless bodhicitta is the entry gate to the Mahayana path, he entered the Mahayana small path of accumulation. When he cultivates wisdom, it is conjoined with emptiness and that makes his mind vast (due to bodhicitta) and profound (due to realizing emptiness). He wishes not to abide in individual liberation (abiding nirvana) but to be free from the extreme of peace (abiding nirvana) as well as from samsara. Therefore, he wishes to achieve non-abiding nirvana, which is the attainment of a buddha.
A Buddha abandoned both afflictive and knowledge obscuration, having generated the path perfection of wisdom (the wisdom of emptiness conjoined with bodhicitta). In his continuum, wisdom and bodhicitta are the same mind: the omniscient mind of a buddha that realizes all objects of knowledge directly, past present and future, in an unmistaken way, etc. He achieved non-abiding nirvana, abiding neither in samsara nor in individual liberation. His enlightened activities are uninterrupted.