Some or all of the tests I write and run are checks for consistency e.g. assert that if I create a new user account, that the account that was created actually has the same name as the name that was submitted in the registration. And now for checking that I implemented a pagination correctly, I suppose I can check that for any given large resultset, getting the "next page", sometimes repeated times and not only once, will eventually lead to the same last page as getting the last page directly (which is done another way than stepping through one page at a time, going directly to the last page in done by using the reversed order and getting the first page from the reversed order.
In our projects we try to follow test-driven development but sometimes I think it is not exact whether a test is a unit test or an integration test when in fact both the integration tests and the unit tests are mostly or only "constistency checks". I didn't see any other type of test than for consistency (both the unit tests and the integration tests do assertions), but it seems that mocking is used more in integration tests than in unit tests and than a unit test is smaller and for a single component or method while an integration test is "larger", but that is still not an exact difference.
So what kind of a test is a consistency check? Is it a unit test or an integration test?