https://www.bitecode.dev/p/testing-with-python-part-5-the-different
I most heartily agree with the point that testing is a spectrum.
I also agree that it doesn't really matter /what/ you call the tests, so long as everyone working on the tests agree (or at least uses the terminology even if they disagree).
I liked unit, functional, and integration - no side effects, some narrow side effects/external deps OK, and there were definitely side effects.