hate vs disdain

hate and disdain both are nouns.

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

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

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

hate (noun)	disdain (noun)
the emotion of intense dislike; a feeling of dislike so strong that it demands action	a communication that indicates lack of respect by patronizing the recipient
	lack of respect accompanied by a feeling of intense dislike

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