What does the difference between sympathy and pity?

Sympathy indicates a geniune feeling of sorrow for another, accompanied by a sense or expression that the sympathetic feels the other person's pain, or has experienced similar pain. Pity is a term that expresses sorrow for another person's troubles, but without the sense of sharing that person's feelings. "I know exactly how you feel; I feel your pain" is a statement of sympathy. "It must be terrible feeling the pain you do" is a statement of pity.

Some people think expressions of pity are condescending in the sense that the people expressing the pity cannot imagine getting themselves into the same situation as the person in trouble. That can come across as a statement of moral superiority. "It must be a terrible thing to be a drug addict. I can't imagine how awful that must be" suggests (especially if you are a drug addict) that the speaker considers himself to be too morally superior to ever get himself into the drug addiction trap. As a result, people have a tendency to express sympathy when what they feel is pity.