cook up vs vamp

cook up is not a noun while vamp is a noun.

Word	Noun	Adjective	Verb	Adverb
cook up	No	No	Yes	No
vamp	Yes	No	Yes	No

As verbs, vamp is a hyponym of cook up; that is, vamp is a word with a more specific, narrower meaning than cook up:

Other hyponyms of cook up include mythologise, mythologize, confabulate, concoct, trump up, spin, vamp up.

cook up (noun)	vamp (noun)
	piece of leather forming the front part of the upper of a shoe
	an improvised musical accompaniment
	a seductive woman who uses her sex appeal to exploit men

cook up (verb)	vamp (verb)
concoct something artificial or untrue	provide (a shoe) with a new vamp
prepare or cook by mixing ingredients	act seductively with (someone)
	piece (something old) with a new part
	make up