quest after vs go after

quest after and go after both are verbs.

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

As verbs, quest after and go after are synonyms defined as:

Other synonyms of quest after include pursue, quest for.

quest after (verb)	go after (verb)
go in search of or hunt for	go in search of or hunt for
	go after with the intent to catch