ANATTA CLARIFIED

In Buddhism, the term anatta (Pali) or anatman (Sanskrit) refers to the idea of "not-self" or the illusion of "self."  On the one hand, it means that what is considered the self, "I," "me," "mine," does not exist ultimately, that it is merely the result of a collection of aggregates, called skandhas, that upon death vanishes.  Hence the self's unreality beyond a person's experience of it in the relative world.

The Sanskrit term anatman, on the other hand, has been interpreted as meaning "no-soul," which can be misleading.  If the word "soul" refers to a non-bodily component in a person that can continue in some way after death, then Buddhism does not deny the existence of a soul.  In fact, persons are believed to possess an ever-evolving consciousness, a stream of consciousness, or a mind-continuity, which, upon death, i.e. the dissolution of the skandhas, becomes one of the contributing causes for the arising of a new group of skandhas.

However, here is the important distinction.  Buddhism denies the existence of a permanent or static entity that remains constant behind the changing bodily and non-bodily (consciousness) components of a living being.  This is contrary to Vedanta that holds that there is a static entity that remains constant throughout, that is eternal, and that is Atman/Brahman.