Testing and debugging are two different processes.
Testing is the process of identifying the failure of implemented code. Executing tests can detect failures that are caused by defects in the software.
Debugging is the process of finding, analyzing and removing the causes of failures in a component or system. By debugging, the developer identifies the problem in the system/application/code.
Once the developer has fixed the bug, a tester re-tests to ensure that the error/bug no longer exists.