hate vs despise

hate is a noun but despise is not a noun.

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

As verbs, despise is a hyponym of hate; that is, despise is a word with a more specific, narrower meaning than hate:

Other hyponyms of hate include abhor, abominate, execrate, loathe, contemn, disdain, scorn.

hate (noun)	despise (noun)
the emotion of intense dislike; a feeling of dislike so strong that it demands action

hate (verb)	despise (verb)
to have and express negative sentiments about a person	look down on with disdain
dislike intensely; feel antipathy or aversion towards