There are quite a few intended meanings of these qualifiers; here are some examples of possible meanings of "I'm sorry," with each interpretation in parentheses.
"I'm sorry, can you tell me where the library is?" (Excuse me...)
"I'm sorry, but that doesn't work for me." (I hate to have to tell you this...)
"I'm sorry, but no." (No matter what you say...)
"I'm sorry, what did you say?" (I beg your pardon...)
"I'm sorry, I just couldn't get there on time." (I have a good excuse if you want to know...)
"I'm sorry, I said vanilla, not chocolate." (Were you paying attention...?)
"I'm sorry, I totally screwed up." (Please forgive me...)
"I'm sorry, but she went to jail?" (I can't believe what you're saying...)
"I'm sorry, I'm busy right now." (Stop bothering me...)
"I'm sorry, I tried to stop him." (It's really not my fault...)
I could come up with even more, but I hope I've made the point that English is tremendously flexible, and that context, inflection, intonation, the situation, and the demeanor of the speaker, all influence meaning to the point that the same two words can mean dozens of different things.