spit up vs exhaust

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

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

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

Other hypernyms of spit up include discharge, eject, expel, release.

spit up (noun)	exhaust (noun)
	system consisting of the parts of an engine through which burned gases or steam are discharged
	gases ejected from an engine as waste products

spit up (verb)	exhaust (verb)
discharge (phlegm or sputum) from the lungs and out of the mouth	wear out completely
give reluctantly	eliminate (a substance)
	use up the whole supply of
	use up (resources or materials)
	deplete