I think we call those "fakes", and reserve mocks for those tests that count the number of times a function was called, yielding "change detector tests".

Personally, I find it best to not be too concerned about the terminology, and make sure your test doubles get the data that the code under test needs to the place that needs it. The more real code you can involve in integration tests, the better; only look at replacing real code with test doubles if there is a performance or reliability downside. Databases have never hit that performance/reliability downside for me; network services do.