cough up vs give

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

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

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

cough up (noun)	give (noun)
	the elasticity of something that can be stretched and returns to its original length

cough up (verb)	give (verb)
discharge (phlegm or sputum) from the lungs and out of the mouth	proffer (a body part)
give reluctantly	consent to engage in sexual intercourse with a man
	occur
	estimate the duration or outcome of something
	dedicate
	convey or communicate; of a smile, a look, a physical gesture
	convey, as of a compliment, regards, attention, etc.; bestow
	bestow
	give entirely to a specific person, activity, or cause
	allow to have or take
	manifest or show
	guide or direct, as by behavior of persuasion
	inflict as a punishment
	accord by verdict
	submit for consideration, judgment, or use
	offer in good faith
	give food to
	propose
	be flexible under stress of physical force
	give or supply
	bring about
	organize or be responsible for
	cause to happen or be responsible for
	perform for an audience
	present to view
	move in order to make room for someone for something
	break down, literally or metaphorically
	transfer possession of something concrete or abstract to somebody
	give as a present; make a gift of
	leave with; give temporarily
	cause to have, in the abstract sense or physical sense
	be the cause or source of
	place into the hands or custody of
	convey or reveal information
	contribute to some cause
	transmit (knowledge or skills)
	endure the loss of
	bestow, especially officially
	deliver in exchange or recompense
	give (as medicine)
	give or convey physically
	afford access to
	emit or utter
	execute and deliver