Being bad is a value judgment; being wrong is making an error. (A recipe can be “bad” without being wrong, i.e. you can follow the recipe without a mistake and still make a lousy soup.)
To be wrong is to be incorrect (such as selecting the wrong answer), while a bad decision is intentionally harmful (to decide not to study for the test).
This distinction (and most language distinctions) matters because those who re-label a “bad” (moral) choice as a “mistake” (incorrect/wrong) will allow them to dodge responsibility.