Hard luck is when something great escapes you; love, fame etc.
Example:
Person A: Did you go out with that guy?
Person B: No, hard luck! He said that he was busy.
Bad luck is when something terrible happens to you ; car crash, house fire, job loss etc.
Example:
Boss: Why are you so late to work?
Worker: A car crashed into the back of my car.
Boss: That's bad luck, are you insured?