Debugging done in the devlopment phase by the devlopers.
Testing is conducted by the testers in testing phase.

In devlopment phase devloper fixes the bug (i.e)called debugging.
In testing phase tester will finds the bug (i.e)called testing to improve the quality of the product

If a defect/error is found by developer side that is called Debug and the process is called Debugging and if any defect is found by tester side is called testing.