Unit tests are too. What the comment you are replying to is referencing is Integration tests, the type that instead of working on a “this class returns this” instead works on “component A calls Component B to do something, are the two still speaking the same language and expectations?”
There's three levels of testing: unit, integration, and end-to-end.
End-to-end (e2e) tests the entire stack: deploy the site with database and all, run a script that visits a page, clicks and stuff, and checks if the right things become visible.
Unit tests are the other extreme: you take a single unit of code and test whether it does what it's supposed to, while mocking all communication with other units of code.
Integration tests are in between those two extremes, and probably the least understood as a result (at least by me). They look like unit tests, and don't generally test the UI, but they don't mock the other components, and ideally also set up a database to test against.
I think there's a bit of overlap between unit and integration tests; a sloppy unit test where you don't mock (some) other components but treat them as part of the unit you're testing, start to look like integration tests at some point. If you want a clear demarcation, I think you might consider a database connection essential to count as integration test.
