'Pity and sorrow' is one of the definitions of the word sympathy, but that's not the meaning generally implied when used in comparison to empathy.
"Sympathy (from the Greek words syn "together" and pathos "feeling" which means "fellow-feeling") is the perception, understanding, and reaction to the distress or need of another human being."[0]
"When you sympathize with someone, you have compassion for that person, but you don’t necessarily feel her feelings."[1]
Generally the difference between empathy and sympathy is the internal response to the feelings of others. If you personally are feeling the same thing as the person, then that's generally empathy, otherwise it's generally sympathy.
"Sympathy (from the Greek words syn "together" and pathos "feeling" which means "fellow-feeling") is the perception, understanding, and reaction to the distress or need of another human being."[0]
"When you sympathize with someone, you have compassion for that person, but you don’t necessarily feel her feelings."[1]
Generally the difference between empathy and sympathy is the internal response to the feelings of others. If you personally are feeling the same thing as the person, then that's generally empathy, otherwise it's generally sympathy.
[0] - https://en.wikipedia.org/wiki/Sympathy
[1] - http://grammarist.com/usage/empathy-sympathy/