quest after vs search

quest after is not a noun while search is a noun.

Word	Noun	Adjective	Verb	Adverb
quest after	No	No	Yes	No
search	Yes	No	Yes	No

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

Other hypernyms of quest after include look for, seek.

quest after (noun)	search (noun)
	the activity of looking thoroughly in order to find something or someone
	boarding and inspecting a ship on the high seas
	an investigation seeking answers
	the examination of alternative hypotheses
	an operation that determines whether one or more of a set of items has a specified property

quest after (verb)	search (verb)
go in search of or hunt for	inquire into
	try to locate or discover, or try to establish the existence of
	subject to a search
	search or seek