Testing an implementation and testing a state

Sometimes I want to test the implementation — like assert that some external calls are done, that some method is called no more than 1 time, or something similar. I usually use unit tests for that.

In case of integration testing — I concentrate more on the state. I care more about the end result of the processed request. I want to assert that some walue returned from external call is saved, that all the needed timestamps are updated and stuff like that.