enmity vs hate

enmity and hate both are nouns.

Word	Noun	Adjective	Verb	Adverb
enmity	Yes	No	No	No
hate	Yes	No	Yes	No

As nouns, hate is a hypernym of enmity; that is, hate is a word with a broader meaning than enmity:

enmity: the feeling of a hostile person
hate: the emotion of intense dislike; a feeling of dislike so strong that it demands action

Other hypernyms of enmity include hatred.

enmity (noun)	hate (noun)
the feeling of a hostile person	the emotion of intense dislike; a feeling of dislike so strong that it demands action
a state of deep-seated ill-will

enmity (verb)	hate (verb)
	to have and express negative sentiments about a person
	dislike intensely; feel antipathy or aversion towards