hazard vs run a risk

hazard is a noun but run a risk is not a noun.

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

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

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

hazard (noun)	run a risk (noun)
an obstacle on a golf course
an unknown and unpredictable phenomenon that causes an event to result one way rather than another
a source of danger; a possibility of incurring loss or misfortune

hazard (verb)	run a risk (verb)
put forward, of a guess, in spite of possible refutation	take a risk in the hope of a favorable outcome
take a risk in the hope of a favorable outcome
put at risk