Yes, there can be a slight (but important) difference between feeling guilty over something we've done wrong and feeling regret over it. Let me explain.
The difference is that it's possible to feel guilty over something we've done wrong but not really regret it. I think, for example, of a man who wrote me recently and said that he had been unfaithful to his wife for several years. Now he was planning to leave his family and marry his lover (who is married also). He admitted he felt guilty over what he was doing–but he also said he had no regrets and intended to go ahead with his plans.
The Bible warns us against this kind of attitude (as I tried to make clear in my reply to him). Guilt and regret should go hand in hand and lead us to repentance. Like the pain we get when we touch a hot stove, they are God's warning to us, telling us to turn from our sin.
Judas felt guilty when he betrayed Jesus, and he even felt regret. But he refused to repent and seek God's forgiveness, and the Bible says he was "doomed to destruction" (John 17:12). Don't let this happen to you, but by faith turn to Christ for the forgiveness you need. The Bible says, "Godly sorrow brings repentance that leads to salvation and leaves no regret" (2 Corinthians 7:10).