Regression testing - after integrating (and maybe fixing) you should run your unit tests again. This is regression testing to ensure that further changes have not broken any units that were already tested. The unit testing you already did has produced the unit tests that can be run again and again for regression testing.
Acceptance tests - when a user/customer/business receive the functionality they (or your test department) will conduct Acceptance tests to ensure that the functionality meets their requirements.
This means it's run after all patches, upgrades, bug fixes. Regression testing can be seen as a special case of combined unit test and integration test.