Regret and Remorse
When dealing with patterns of difficult behavior the question arises: What demonstrates a conversion or change of heart versus just a change in tactics ('hoovering')? Well, an important clue is contained in whether the reaction to being confronted is an expression of regret (everyone is capable of this) or is a demonstration of remorse (pretty rare in our culture, let alone from difficult people). Apologies are generally meaningless in themselves, what is important is whether they arise out of regret or remorse. It is also useful to contrast regret and remorse with state shame.
Regret
This is a self-sorrowful emotion, the intensity of which may vary from mild to deep. The regretful person has sorrow for themselves about the consequences of their decisions and actions. Regret may recognize or even be spurred by the consequences to others, but the focus is on the self. All people have regrets--it is human nature to want everything to turn out well and be distressed when it doesn't. Regret of course can also easily be insincere since there are no actions or sacrifices intrinsically flowing from it.
Remorse
This is an other-sorrowful emotion which is never mild. It usually co-exists with regret but is much more. Remorse instills the person with a willingness and energy to concretely address consequences and make amends. Actions naturally flow from remorse, and there is a eagerness, and humility in discussing what happened. A remorseful person will not blame the victim(s) and will insist on taking responsibility.