The list of things 'I'm sorry' can mean:
1a. 'I apologize for doing X; I knew it was wrong but I did it anyway, but I won't do it again'
1b. 'I apologize for doing X; it was an accident/out of ignorance, and I won't do it again'
2. 'I don't apologize for doing X, but I regret that X hurt you'
3. 'I wish this situation that is out of my control were otherwise so it wouldn't hurt you'
These are all subtle differences, but cause huge misunderstandings and warpings of social dynamics. Example: my dad, who was a depressed basket case for most of my life (fortunately he's getting better now) would always apologize for things with the intention of meaning (3), but inflecting it like meaning (1), which drove me and my mom crazy because he always seemed to be taking responsibility for the whole world. (2) is also an important distinction: for example, I once did something that could be construed as betraying person A; I am really sorry it hurt A, but don't regret doing it because it was something I needed to do.
Problem is if you go around saying the expanded forms, people will look at you funny. Here we are with the most sophisticated language on earth (at least if you measure it by vocabulary, which theoretically correlates somewhat to number of concepts you can express) and we still get this damned vagueness all over the place.