Re-Testing:
Re-testing is done by the tester after a bug/issue is fixed or resolved for checking that application works properly or not as per requirement specification or not.
If Tester found that bugs/issues are not resolved or fixed, He/She updates the status of bugs as “RETEST FAILED” and assigns the bug to developer again.
It is something that testing the application again after getting the fixed the defects from the developer.
Regression Testing:
In Regression testing Tester needs to test all features and functionality again as well as existing functionality of application should not be hampered/broken due to addition of new features.
Regression testing is used to check the existing functionality is working fine or not broken due to the implementation of newly added functionality or changes in new code.
For Example: Test that existing feature of Twitter application is working fine or not due to implementation of newly added functionality as”X”