After a defect is detected and fixed, the software should be re-tested to confirm that the original defect has been successfully removed. This is called confirmation. Debugging (defect fixing) is a development activity, not a testing activity.
Regression testing is the repeated testing of an already tested program, after modification, to discover any defects introduced or uncovered as a result of the change(s). These defects may be either in the software being tested, or in another related or unrelated software component. It is performed when the software, or its environment, is changed. The extent of regression testing is based on the risk of not finding defects in software that was working previously.