Notes

Pity expresses a negative evaluation of the bad situation of others. Pity is more spectator-like, where we can pity people and maintain a safe emotional distance. The belief that the person/thing is inferior. When you pity, you are conscious of how bad that situation is and you compare it to yourself, so you feel better about yourself. Pity is just feeling sorry for someone. Sometimes so, that you help them because you make yourself out as superior, you may be "higher up in a way" and probably should help.

Compassion involves far greater commitment with feeling bad with the person that feels bad(pity feel bad 'for' someone vs 'with' them). To actually feel someone's pain is to be empathetic, and to be passionate to help that person create a different experience. Compassion allows equality in having the connection with someone humanly, empathizing. Showing compassion means being there for another without judgment—being a pillar next to which they can stand.

This is probably just a shallow dip into the differences. Though I have a bit of a feeling that compassion may actually just be two sided, which is why it's misunderstood a lot. But that's a different discussion.