vomit up vs puke

vomit up is not a noun while puke is a noun.

Word	Noun	Adjective	Verb	Adverb
vomit up	No	No	Yes	No
puke	Yes	No	Yes	No

As verbs, vomit up and puke are synonyms defined as:

Other synonyms of vomit up include barf, be sick, cast, cat, chuck, disgorge, honk, purge, regorge, regurgitate, retch, sick, spew, spue, throw up, upchuck, vomit.

vomit up (noun)	puke (noun)
	a person who is deemed to be despicable or contemptible
	the matter ejected in vomiting

vomit up (verb)	puke (verb)
eject the contents of the stomach through the mouth	eject the contents of the stomach through the mouth