sputter vs cough up

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

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

As verbs, cough up is a hypernym of sputter; that is, cough up is a word with a broader meaning than sputter:

Other hypernyms of sputter include cough out, expectorate, spit out, spit up.

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

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