I think what you are asking is what is the scope of each test phase.
Different definitions exist in the minds of different people, however, I think a general rule is:
system test: - Ensuring that the functionality of the application under test (AUT) works as per the functional design of the system (if no design documentation exists then this becomes slightly more difficult).
Integration Test: a much wider range of definitions. Integration Test in the Small is about ensuring that the components/modules/programs of the AUT can owkr together in an integrated fashion
Integration Test in the Large is to ensure that the AUT's interfaces with other application work correctly.
You might have to build some test harnesses (simulate other parts of the system) to correctly perform integration testing (both large and Small)
if you require more details then please repost with specific questions and I'll try and be more detailed