desire vs quest

desire and quest both are nouns.

Word	Noun	Adjective	Verb	Adverb
desire	Yes	No	Yes	No
quest	Yes	No	Yes	No

As verbs, quest is a hypernym of desire; that is, quest is a word with a broader meaning than desire:

Other hypernyms of desire include ask for, bespeak, call for, request.

desire (noun)	quest (noun)
an inclination to want things	the act of searching for something
the feeling that accompanies an unsatisfied state	a search for an alternative that meets cognitive criteria
something that is desired

desire (verb)	quest (verb)
feel or have a desire for; want strongly	seek alms, as for religious purposes
express a desire for	express the need or desire for
expect and wish	bark with prolonged noises, of dogs
	search the trail of (game)
	make a search (for)