Anatta is a Buddhist doctrine stating there is no permanent self. Under Anatta, the self consists of a constantly changing body, soul, and consciousness. Followers of Anatta believe attachment to a permanent self is seen as the root of suffering, and liberation (Nirvana) comes through realising the constantly changing nature of life and the self. In practice, it looks like avoiding attachment to relationships, being materially minimalist, and believing one's self is never truly "fixed".
Śassata-vāda (eternalism) is a doctrine stating the self is everlasting, unchanging, and absolute. Followers of Śassata-vāda believe the only way to achieve true liberation is through self-realisation by seeking out the meaning of one's internal identity. In practice, it looks like the pursuit of desire and active experimentation to discover what speaks most truly to one's "fixed" self.