Regret would mean that they wish they could go back and not do it again, and they definitely won't do it again in the future. But some people say sorry as if that alone will fix everything. They don't really regret it and will do it again. That's not truly sorry.
As for saying mean things...we really can control what we say. If we know ourselves to say mean things in anger, we can just choose to cool off before discussing something, or enroll in some anger management classes. There are not many words that mean less than empty sorries.