This might be sort of the difference between sympathy and empathy though.. both actually are inclusive of each other. Feeling 'sorry for' includes a level of compassion, and feeling compassion includes a level of sympathy.
So here is my best idea on the difference between the two. My T always says to try to have compassion for myself - and I consider compassion to be being genuinely sensitive to. Doing things I like on purpose, being nice to myself on purpose. Where feeling sorry would be having thoughts like "why me/poor me" in a way (those aren't the words I want to use but they are the best I have right now) but it does include compassion because it's validating that it's something difficult. I see feeling sorry as feeling 'about' something where compassion is feeling/doing 'for' something.
That's just my crackpot theory based on what I do for myself