Short answers, pulled from the story.
Nirvana, also spelled nibbana in Pali, refers to the extinguishing of the three poisons of greed, aversion, and delusion, leading to release from the cycle of rebirth known as samsara. It is regarded in all forms of Buddhism as the highest religious goal and is described as unconditioned, beyond time and space, and outside the realm of dependent arising.
Sopadhishesa-nirvana, or nirvana with remainder, is attained during life when the three fires are extinguished but the body and five aggregates remain. Anupadhishesa-nirvana, or parinirvana, is the final nirvana at the moment of death, when there is no fuel left and the aggregates cease entirely.
Apratishtita-nirvana, or non-abiding nirvana, is the Mahayana view of a Buddha's attainment, attributed to the Yogacara scholar Asanga, likely active in the fourth century CE. It describes a state in which a Buddha has eradicated both afflictive obstructions and obstructions to omniscience, enabling them to remain active in samsara out of compassion rather than dwelling in static cessation.
Buddhaghosa, the fifth-century Theravada exegete, argued in his Visuddhimagga that nibbana is apprehensible by noble ones through virtue, concentration, and understanding. He rejected the view that nibbana is a mere absence or nothingness, arguing that if it were simply an absence, the Buddhist path would be meaningless.
The Sarvastivada school held that nirvana was a real existent, dravyasat, that perpetually protected a series of dharmas from defilement across past, present, and future. The Sautrantikas rejected this, treating nirvana as a conventional designation without intrinsic nature, defined simply as the non-arising of further latent defilement once existing defilements had been extinguished.
The tathāgatagarbha doctrine, which probably appeared toward the later part of the third century CE, holds that all sentient beings contain a Tathagata as their essential inner nature. It connects to nirvana through the idea that Buddha-hood is already innate but covered by adventitious defilements, and the Mahāparinirvāṇa Sūtra presents nirvana in this framework as possessing permanence, bliss, the self, and purity.