Difference between abiding nirvana and non-abiding nirvana? 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.
Non-abiding Nirvana is a standard Mahayana doctrine, described as non-abiding in contrast with (Hinayana's) Nirvana which is considered abiding.

(As always, I have to remind everyone that Theravada is NOT equivalent to Hinayana. Hinayana refers to a primitive level of understanding of Dharma. There are Mahayana practitioners still on Hinayana levels; There are Theravada practitioners on Mahayana level.)

In Hinayana thinking, beginner thinking, we imagine Nirvana as some state we achieve or some place we enter ONCE AND FOREVER. In Hinayana-level thinking, first you get rid of coarse turbulence in your life, then you quit society and spend most of your time in meditation, then you basically give up worries about all kinds of things, then you go through Jhanas, so in the end you achieve this 100% peaceful 100% quiet 100% perfect mind - with no conflict, no dukkha whatsoever, and you enter and dwell in that state. This is abiding nirvana.

This is because, in Hinayana thinking, you can't, for example, be in society, have job, family etc. - and be in Nirvana. Can't happen, because regular life creates too many disturbances, too many conflicts and issues. On this level of understanding, you despise disturbances, conflicts, and issues - because they disturb your peace, they break your attempts at stabilizing your mind and attaining some semblance of Nirvana. You keep craving a perfect peace, perfect suchness - which is how you imagine Nirvana to be. This perfect peace is Abiding Nirvana.

In contrast to that, on Mahayana level, we achieve the real Nirvana that the Buddha taught (in Pali Canon, too) - the unconditional, non-abiding Nirvana. Non-abiding Nirvana means that we do not abide, do not dwell, in any single position or state of mind. We no longer get disturbed by the circumstances because we have mastered the dynamic equilibrium of non-craving and non-attachment. We do not feel that life interferes with our practice or interferes with our peace, because on this level, life IS peace, life IS nirvana - if you are not attached to a particular shape or  position.

On the traditional gradual path, the non-abiding Nirvana is attained as the last step of the gradually perfecting the mind of peace. It is attained through transcending the very duality of sukkha/dukkha, the very duality of suchness/wrongness.

It's like, first we get rid of coarse disturbances and conflicts, then smaller and subtler ones, this is described as the progression of jhanas - and on each level the very things that we thought were important for practice are now considered obstacles that should be let go. So on some level you learn to use positive thinking aka self-suggestions (vitakka/vicara), you learn to change your perspective - and once you get good at that, you outgrow it and on that level using self-suggestion seems very artificial - and yet you have to master it first. Then on the next level, you apply pyschosomatic methods - like breathing, working with energies. Then you master that and transcend it too; now it seems artificial and contrived to the new you. Then you practice being emotionally sober, get good at that, outgrow it. Then you practice pure mindfulness, which is basically pure suchness. And theeeeeeeeeeeeen your practice gets so thin, so perfectly refined, that your mindfulness and your suchness is present all the time, regardless of what you're doing, regardless of you paying attention or not. At the same time, your insight into Emptiness reaches maturity and you penetrate the notion of right vs. wrong deeply, you really get the principle of relativity, you understand the limit of suchness. This is when the magic moment occurs....

Once you clearly see the limit of suchness AND your mindfulness is ever-present, your practice gets so thin as to basically disappear. From this moment on, everything is your practice, and everything is Nirvana, regardless of how things change in the world.

By this time, there is no separation between Nirvana and Samsara, no limits to suchness, all conceptual dualities are transcended. So whatever life throws at your is fine, whatever happens, happens. You have no position, no shape, nothing to regret - you can't be pinned down. You are neither coming nor going, you're invisible and neither regular humans nor gods can recognize you because you don't look any different.

Nothing can be said about anything at this point, because all descriptions require a base for assertion, but there is no such base anymore. Everything is... just is. IS.

But life goes on. And this is non-abiding Nirvana.