cough vs spit out

cough is a noun but spit out is not a noun.

Word	Noun	Adjective	Verb	Adverb
cough	Yes	No	Yes	No
spit out	No	No	Yes	No

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

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

cough (noun)	spit out (noun)
a sudden noisy expulsion of air from the lungs that clears the air passages; a common symptom of upper respiratory infection or bronchitis or pneumonia or tuberculosis

cough (verb)	spit out (verb)
exhale abruptly, as when one has a chest cold or congestion	spit up in an explosive manner
	discharge (phlegm or sputum) from the lungs and out of the mouth
	utter with anger or contempt