Caveat: test terminology is not very standardized

End to end tests

Focused on business requirements.

Exercise the complete flow, including external systems.

Usually these tests are slow to execute.

Acceptance tests

Focused on business requirements.

Exercise all parts of the flow in our system. Compromise on feedback and speed of execution.

Faster than end to end tests, but not as thorough.

Integration tests

Focused on technical implementation.

Exercise parts of our system that connect with external systems.

Can be slow to execute, depending on external system and the integration with it.

Unit tests

Focused on atomic behaviors.

Exercise parts of the flow in our system.

Very fast to execute.

(src: Book: Agile Technical Practices Distilled - Pedro, Marco, Alessandro)