run out vs exhaust

run out is not a noun while exhaust is a noun.

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

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

Other hypernyms of run out include consume, deplete, eat, eat up, expend, run through, use, use up, wipe out.

run out (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

run out (verb)	exhaust (verb)
use up all one's strength and energy and stop working	wear out completely
prove insufficient	eliminate (a substance)
exhaust the supply of	use up the whole supply of
become used up; be exhausted	use up (resources or materials)
flow, run or fall out and become lost	deplete
flow off gradually
leave suddenly and as if in a hurry
lose validity