cough up vs sputter

cough up is not a noun while sputter is a noun.

Word	Noun	Adjective	Verb	Adverb
cough up	No	No	Yes	No
sputter	Yes	No	Yes	No

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

Other hyponyms of cough up include cough, ptyalise, ptyalize, spew, spit, spue, spit out, splutter.

cough up (noun)	sputter (noun)
	an utterance (of words) with spitting sounds (as in rage)
	the noise of something spattering or sputtering explosively

cough up (verb)	sputter (verb)
discharge (phlegm or sputum) from the lungs and out of the mouth	spit up in an explosive manner
give reluctantly	cause to undergo a process in which atoms are removed
	utter with a spitting sound, as if in a rage
	climb awkwardly, as if by scrambling
	make an explosive sound