The central difference between empathy and sympathy is that someone feeling empathy is able to recognize and share someone else's perspective, whereas someone feeling sympathy is just concerned for the other person's plight. Knowledge of the other person's struggle is vital with empathy, but is not necessary with sympathy.
Often, when someone feels empathy, it is because that person either wants to or is obligated to assist in resolving the subject's situation. In contrast, someone feeling sympathy usually has pity for the other person and desires for a problem to be resolved, but isn't directly involved. Sometimes, people use empathy to understand the emotions of others in order to manipulate and cause harm. With sympathy, feelings center on concern for another person's well-being.