What the manifest is
The Coalition for Content Provenance and Authenticity defines a format for attaching provenance claims to media. A manifest holds assertions: who created the asset, with which tool, and which edits were applied, each recorded as an ingredient.
Those assertions are signed, so a verifier can check that the manifest was not altered after signing, and can see which certificate signed it.
Content Credentials is the consumer-facing name for the same idea, popularised by Adobe. It is one implementation of C2PA, not a separate standard.