Integration Tests are Tests that should be run in an automated test Environment.
In contrast, manual tests should not run in an automated test Environment.
The Manual Test Annotation should be used for Tests that either needs to be executed manually or where third Party Applications are needed for Testing.
Beside the Annotation for Integration and ManualTest there are some more like DemoTest and PerformanceTest
See also https://help.sap.com/docs/SAP_COMMERCE/d0224eca81e249cb821f2cdf45a82ace/aae25ecb74ab4bd69cc5270ffd45... for more Information