Anna Filina has a new post to her site that helps to clarify the definitions between functional, unit and integrations tests of your application's functionality.
I have recently read a blog post claiming that functional tests are not "true" tests. The author also claims that unit testing shows you where the problem is occurring, while functional testing simply identifies that a problem exists. This argument is deceptive and the conclusion dangerous. Different kinds of tests are not mutually exclusive. One is not superior to the other. They have different goals and can happily coexist. Let me explain the kinds of tests so that you could make enlightened decisions.
She covers each type of test in detail, noting the goal of that particular type and some examples of the kinds of things they might test. She starts with the highest level, functional testing, then jumps down to the lowest - unit testing. She finishes up the post defining "integration tests" as tests that ensure you're integrating correctly - that you're using the API provided by the tool in the right way and that it's working as expected.