One category of ethics is about minimizing harm to others. In this take the goal of the ethical person is to try to limit the amount of damage they cause to other persons. This is easy to measure when the damages are physical but harder when it's "emotional damages". For example the concept of micro-aggressions is quite new and yet this idea indicates that according to some people units of harm can occur by seemingly innocuous speech, statements, or behaviors. This highlights one of the problems with harm minimization which also can apply to something like the non aggression principle which itself is a type of harm minimization heuristic.
When the word "aggression" is used we have to decide what that means. It's obvious when it's physical but it's not as obvious when it's not physical. If we take on the heuristic of non aggression principle it can lead to pacifism as a strategic method of minimizing violence in the world. Pacifism looks ethical but the problem is how do you apply this in a violent world where others don't also apply the same principle? In a world of live and let live, where everyone follows the same rules, and have the agreement on what is or isn't aggression, maybe it can work (such as within a family).
What is the distinction which makes regret minimization different? Minimizing regret is more about how the individual person treats their future self. Doctors are taught to practice harm minimization but this is a very conservative strategy which does not encourage risk taking. Regret minimization can inform the practitioner when it makes sense to take a risk. If you ask yourself "if I don't take this opportunity will my future self regret it?" and then of course it's subjective how much you'll regret having not done something. Just as you can regret having done something you can also regret having not done something.
Regret minimization can allow a person to take risks while harm minimization doesn't encourage risk taking. If all you are concerned about is the amount of harm you do to others then the way to reduce the risk of upsetting other people is to not do anything at all or to do the least disruptive thing. The problem with this is then you can regret that you didn't do all you could have done to put your future self in a position of less regret.
Neither of these ways of ethical thinking is perfect and I've had phases where I've given more emphasis on one or the other. In general if you can get as much as you can from the world while doing the least harm it's great. What if you can't avoid the risk of harming others? For example an earlier version of myself could have thought that paying taxes was potentially harmful (because the government was in a war I didn't agree with), and in a harm minimization type of thinking does this mean I should stay poor so I pay less taxes and can do the least harm? Of course I didn't go down that path ultimately, because then I'd have regrets such as not having the chance to live a decent life.
So in conclusion harm minimization is great but taken to the extreme it can result in the individual damaging their future self by giving future versions of themselves regret. On the other harm regret minimization takes into account what the future self might feel or experience and factors that into the decisions made today. I think harm minimization can work in certain contexts but it would be nearly impossible to live a modern life with harm minimization as the only ethical strategy unless someone lives as a monk or a priest. At the same time if the world falls into a conflict the harm minimization isn't going to protect the future self from the consequences of that conflict so again regret minimization seems to win out in long term ethical strategy.
