Yees I have a better idea of their differences now
Feeling guilty would be more like feeling bad for having done something that could make others judge us.
You hurted x, you are a bad person.
'' Fuck, now people will be mad at me. I'm not as good as I'm supposed to be. I have to do something '' .
Therefore the person says she's sorry to correct the situation and make herself look good again, even if she feels more guilty than she feels sorry.
Feeling sorry would be like
Aaaaaw, I hurted x. X must feel so bad. I have to do something so that x is good again.
But it's very close to guilt ain't it. Meant that way, I think you can feel guilty without feeling sorry, but you can't feel sorry without feeling guilty. Didn't want to hurt x and feeling bad for it but also feeling bad/guilty because x and some others might be mad.
Then there is the other use of the word sorry, wich is empathy. Feeling sad for the pain of others when we aren't to blame for it in any way or when the event happened so long ago that it doesn't bring strong emotions of guilt anymore.