empathy vs sympathy

empathy and sympathy both are nouns.

Word	Noun	Adjective	Verb	Adverb
empathy	Yes	No	No	No
sympathy	Yes	No	No	No

As nouns, sympathy is a hypernym of empathy; that is, sympathy is a word with a broader meaning than empathy:

empathy: understanding and entering into another's feelings
sympathy: sharing the feelings of others (especially feelings of sorrow or anguish)

Other hypernyms of empathy include fellow feeling.

empathy (noun)	sympathy (noun)
understanding and entering into another's feelings	an inclination to support or be loyal to or to agree with an opinion
	sharing the feelings of others (especially feelings of sorrow or anguish)
	a relation of affinity or harmony between people; whatever affects one correspondingly affects the other