Short answers, pulled from the story.
Anattā is the Buddhist doctrine of non-self, asserting that no unchanging, permanent self exists and that there is an absence of essence in any phenomenon. The term is a composite Pali word from "an" (not) and "attā" (self-existent essence). It is one of the Three Marks of Existence, alongside dukkha (suffering) and anicca (impermanence).
In Hinduism, Atman is the eternal, unchanging observing awareness or witness-consciousness at the core of each being. Buddhism's anattā directly rejects any such permanent essence; the Buddhist Suttas apply non-Self to literally everything, including Nirvana, whereas the Upanishads held that a real Self could be found and known to be identical to Brahman.
Scholars are divided. Richard Gombrich and Alexander Wynne argue that early Buddhist texts such as the Anattalakkhaṇa Sutta do not deny a self outright but present a "not-self" teaching that was later interpreted as a "no-self" teaching. Johannes Bronkhorst suggests the texts clearly reject seeking Atman-like self-knowledge as the path to liberation, without necessarily denying the soul's existence.
The Buddha held anattā alongside belief in karma and rebirth, rejecting both the eternalist view (an unchanging essence underlies moral continuity) and the annihilationist view (death is total dissolution with no rebirth or karma). Anattā does not mean there is no afterlife or no fruition of karma; Buddhism explicitly contrasts itself with annihilationist schools such as Charvaka.
The Dhammakaya tradition in Thailand teaches that nirvana is atta, or true self, not no-self. In 1994, scholar monk Ven. Payutto criticized this as heretical, stating that the Buddha taught Nibbana as being no-self. The 12th Supreme Patriarch of Thailand had put forward a similar true-self interpretation in 1939.
Nāgārjuna, the founder of the Madhyamaka school active around 200 CE, asserted in chapter 18 of his Mūlamadhyamakakārikā that there is no substantial self and that the Buddha taught the doctrine of no-self. He linked the notion of self to pride, selfishness, and bondage, and taught that accepting emptiness (śūnyatā) dissolves all such obsessions.