I've never really found this to be the case in practice. When I look at well-written unit tests and well-written integration tests, they're usually doing exactly the same sort of thing and have very similar concerns in terms of code organisation and test structure.
For example, in both cases, the tests work best if I test the subject under test as a black box (i.e. interact only with its public interface) but use my knowledge of its internals to identify the weaknesses that will most require testing. In both cases, I want to structure the code so that the subject under test is as isolated as possible - i.e. no complex interactions with global state, no mocking of unrelated modules, and no complex mechanism to reset anything after the test is done. In both cases, I want the test to run fast, ideally instantaneously, so I get immediate results.
The biggest difference is that it's usually harder to write good integration tests because they're interacting with external systems that are generally slower and stateful, so I've got to put extra work into getting the tests themselves to be fast and stateless. But when that works, there's really not much difference at all between a test that tests a single function, and a test that tests a service class with a database dependency.