Tor: What is the difference between “New Circuit” and “New Identity”?

Short answer

On desktop Tor Browser, New Circuit for This Site reloads that site through a different circuit and may help with a broken or blocked exit path. It does not clear cookies or unlink your activity. New Identity closes tabs, clears private browser state, and starts new circuits for later activity. Use New Identity when you need a clean separation between browsing sessions.

Sources

Tor Project: Managing identities, Tor Project: Known issues.