Compassion and Pity seem similar because they mean you feel something good for the person or animal that you're feeling either pity or compassion for and want to make their situation better.
However the difference between pity and compassion is that compassion is a feeling of mercy, empathy, and a desire to help the suffering person or animal out of their bad situation.
And Pity is where you share the problems and suffering with the other person or animal as well as sympathy and sometimes you might also want to help that person or animal out of their situation but you're in a bad situation yourself and cannot do much or anything at all to help them.