API doesn't imply integration. Consider any module or package to have an API exposed to the user of the package. Unit tests should assert that the package behaves as expected.
By users I assume you mean other developers who use the API (including you next week). It would be better to use a different term as often user means "end user" or "customer" and not internal users.
Yeah, I'm not sure what the better word is. As a programmer, I use APIs. "interact with", "code to/against". I think "user" is OK. We're all users at different levels of abstraction.
