This site gives a good definition of State Verification and Behavior Verification as it concerns our efforts to establish unit tests for all new functionality.
Heres the one line definition for each if you want the 50,000 foot view.
State Verification: We inspect the state of the system under test (SUT) after it has been exercised and compare it to the expected state.
Behavior Verification: We capture the indirect outputs of the SUT as they occur and compare them to the expected behavior.
Its a subtle but important distinction in that with state verification you may run a series of method call or processes and verify the expected state of the system after all the call have been made. With behavior verification you are interested in verifying that individual method calls are made to components within the system under test including dependent components utilized by the system under test.