'Guilt' is when you blame yourself for something that you did which was wrong. There is often a moral dimension to it - maybe you hurt someone in some way, or caused problems for others. Guilt is when you hold yourself responsible for something. 'Regret' is simply wishing that you had done something or hadn't done something.

It's hard to explain. I'll try: 'guilt' is a bad feeling as a result of an action that you think was wrong OR that caused someone else pain. However, if you could do it a gain, you would probably choose the same action. 'regret' is a bad feeling as a result of an action that you wish you could change. You believe that you made the wrong choice. For example, if you break up with someone, you may feel guilty because they are in pain. However, if you think you made the right choice, you will not feel regret. IF you decide later that you made the wrong choice and should NOT have broken up with them, you will then feel regret because you made the wrong choice.