exhaust vs cough out

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

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

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

exhaust (noun)	cough out (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

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