Regression testing is a test suite that is designed to cover as much of your application's functionality as possible.
The idea is that when you make a modification to your application, such as to remedy a bug or add new functionality, regression testing will ideally discover any issues (or regressions).
Because the great majority of tests were added in response to previous problems, you have regressed to a previous state if they detect a problem (in which the problem once again exists).
Regression testing, in other words, examines your application.
Mutation testing involves inserting tiny faults (called mutations) into your program (errors that aren't supposed to fix bugs or add new functionality) to check if your test suite detects them.
The premise is that if your test suite fails to detect mutations, it is insufficient and needs to be supplemented with additional test cases. Mutation testing, in other words, evaluates your test suite rather than your application.