Much of the difference between unit and integration testing relates to the scope of the code being tested and the goals of the test. Chances are you have been mixing a combination of the two on Force.com without realizing it.
First, let's consider this definition of Integration testing by Wikipedia:
Integration testing (sometimes called integration and testing, abbreviated I&T) is the phase in software testing in which individual software modules are combined and tested as a group. It occurs after unit testing and before validation testing. Integration testing takes as its input modules that have been unit tested, groups them in larger aggregates, applies tests defined in an integration test plan to those aggregates, and delivers as its output the integrated system ready for system testing.
In general, most published guidance on writing Apex tests falls into this integration testing category. Indeed, the only way to cover Apex Trigger code...