splutter vs cough up

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

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

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

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

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

splutter (verb)	cough up (verb)
spit up in an explosive manner	discharge (phlegm or sputum) from the lungs and out of the mouth
utter with a spitting sound, as if in a rage	give reluctantly