Unit Tests and Integration Tests are orthgonal to each other. They offer a different view on the application you are building. Usually you want both. But the point in time differs, when you want which kind of tests.
The most often you want Unit Tests. Unit tests focus on a small portion of the code being tested - what exactly is called a unit is left to the reader. But te purpose is simple: getting fast feedback of when and where your code broke. That said, it should be clear, that calls to an actual DB is a nono.
On the other hand, there are things, that can only be unit tested under hard conditions without a database. Perhaps there is a race condition in your code and a call to a DB throws a violation of a unique constraint which could only be thrown if you actually use your system. But those kinds of tests are expensive you can not (and do not want to) run them as often as unit tests.