spew vs cough up

spew and cough up both are verbs.

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

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

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

spew (verb)	cough up (verb)
eject the contents of the stomach through the mouth	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
eject or send out in large quantities, also metaphorical