cough up vs spit

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

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

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

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

cough up (noun)	spit (noun)
	the act of spitting (forcefully expelling saliva)
	a skewer for holding meat over a fire
	a clear liquid secreted into the mouth by the salivary glands and mucous glands of the mouth; moistens the mouth and starts the digestion of starches
	a narrow strip of land that juts out into the sea

cough up (verb)	spit (verb)
discharge (phlegm or sputum) from the lungs and out of the mouth	expel or eject (saliva or phlegm or sputum) from the mouth
give reluctantly	utter with anger or contempt
	drive a skewer through
	rain gently