detest vs disdain

detest is not a noun while disdain is a noun.

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

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

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

detest (noun)	disdain (noun)
	a communication that indicates lack of respect by patronizing the recipient
	lack of respect accompanied by a feeling of intense dislike

detest (verb)	disdain (verb)
dislike intensely; feel antipathy or aversion towards	reject with contempt
	look down on with disdain