run a risk vs risk

run a risk is not a noun while risk is a noun.

Word	Noun	Adjective	Verb	Adverb
run a risk	No	No	Yes	No
risk	Yes	No	Yes	No

As verbs, run a risk and risk are synonyms defined as:

Other synonyms of run a risk include adventure, chance, gamble, hazard, take a chance, take chances.

run a risk (noun)	risk (noun)
	a venture undertaken without regard to possible loss or injury
	the probability of being exposed to an infectious agent
	the probability of becoming infected given that exposure to an infectious agent has occurred
	a source of danger; a possibility of incurring loss or misfortune

run a risk (verb)	risk (verb)
take a risk in the hope of a favorable outcome	expose to a chance of loss or damage
	take a risk in the hope of a favorable outcome