The way I think about it is that a punishment is something contrived by a parent to make a child feel bad about something he or she has done wrong. A natural consequence, on the other hand, is something that happens as a direct result of the wrongdoing. In theory, natural consequences are better, because they teach a child that it is the wrongdoing itself that causes the unpleasantness (rather than just getting caught or having a mean mom). Of course some natural consequences are too awful to be allowed, and some are just impractical.