Regret is a longing to undo a past decision, the wish that another choice had been made. Guilt is a related, but not identical, emotion.
In regret, the moral quality of the past decision is not the central factor. A person can regret making a choice because of the consequences of that choice, even if the choice was the morally correct one to make. For a person feeling regret, the outcome is the point.
When the emotion of guilt emerges, morality is at the heart of the matter. People can feel guilt even if they do not regret the choices they have made. Guilt is the feeling that a decision was in some sense morally wrong.
A person who feels guilt identifies their actions as morally wrong. Nonetheless, a guilty person can decide that they would not take back their bad actions, even if they had the opportunity to do so. In this way, feeling guilty can become like a form of self-centered silent punishment, as if the feeling of guilt itself can somehow atone for the harm that a morally wrong decision has resulted in.
While regret contains within it the strong hope that a bad decision will not be repeated, a guilty conscience can lead to the repetition of a wrong choice. When a judgment of guilt is linked with the conclusion that a person is morally flawed because of some kind of inherent character defect, the implication is that the guilty party can be expected to be guilty again. Nonetheless, inherent moral flaws are not a necessary part of a guilty feeling. The emotion of shame is different from guilt in that people who feel shame believes not just that they have made a bad choice, but that they are themselves bad, that there is something wrong with them, in the very core of their identity.
Feeling responsible and taking responsibility are not the same thing. Feeling guilty of a wrong action does not imply that the very same wrong action would not be chosen again.