These 2 terms are not same and there is a difference between Regression and Re-Testing.
Here is what they mean:-
Regression: To test a module or part of software to make sure that the fix done by the developers haven't affected any related component and introduced a new bug. Because this is a very common scenario where you as a tester has reported a bug and when the developers fixed it, some other functionality dependent or related to the same module stopped working now.
So regression testing is to repeat the test to make sure that the original defect is fixed and it hasn't created issues for any other module or dependent component.
Re-Testing: Suppose you have reported a defect and when it's fixed, it will obviously come back to you for re-testing. It's that simple, to re-test a defect which has been fixed now and you are just verifying that it isn't there any more.