"Sorry" or "excuse me" are both often used for the "etiquette", as politeness formulas, nothing more, empty of their emotional meaning. "I'm sorry I have to squeeze past you." There are some cultures/languages (the ones that I know are Native American) where politeness formulas like "hello", "goodbye" or "sorry" (when not ment as a feeling) don't exist, and to whom it is a bit strange, nonsense.
Otherwise it can also mean "it is sad" or "I find it sad", without the regret, repenting aspect; to express concern like in "I'm sorry your mother died", "I'm sorry that the train was late" (and you had to wait for me) or "I'm sorry you don't like what I'm doing". Like in "I'm sorry I hurt you" that your cheated ex-girlfriend would maybe have expected (just an assumption): "I find it sad that I hurt you but I have no regret since it taught me about myself and I assume the consequences of it.
And it can be used in the way you use it, to express regret.
It seems to me that when people use it to express meant feelings, regret or not, they add something more to just "Sorry for..." (in conversations, at least).
But in any case, the most important is to understand and to be understood correctly, imho.
