grill vs cook out

grill is a noun but cook out is not a noun.

Word	Noun	Adjective	Verb	Adverb
grill	Yes	No	Yes	No
cook out	No	No	Yes	No

As verbs, cook out is a hyponym of grill; that is, cook out is a word with a more specific, narrower meaning than grill:

Other hyponyms of grill include barbecue, barbeque, hibachi, broil, oven broil.

grill (noun)	cook out (noun)
a framework of metal bars used as a partition or a grate
a restaurant where food is cooked on a grill

grill (verb)	cook out (verb)
cook over or under a grill	cook outdoors on a barbecue grill
examine thoroughly