In Hinduism, Atman is seen as being the true Self or Essence of a person. To achieve liberation, they have to reach the level of self-knowledge that allows their Atman to become the same as the Brahman.
In Buddhism, there is no concept of the inner Self in Buddhism; although, the word is sometimes used to refer to an Absolute rather than to an individual’s own Self.
Upon death, it is believed a person’s Atman either goes with them to their new life, or it reaches moksha and is freed from the constraints of the death and rebirth cycle. This latter event only occurs when the person understands that their Atman is identical to the Brahman.