barbecue vs grill

barbecue and grill both are nouns.

Word	Noun	Adjective	Verb	Adverb
barbecue	Yes	No	Yes	No
grill	Yes	No	Yes	No

As verbs, grill is a hypernym of barbecue; that is, grill is a word with a broader meaning than barbecue:

barbecue (noun)	grill (noun)
a rack to hold meat for cooking over hot charcoal usually out of doors	a framework of metal bars used as a partition or a grate
a cookout in which food is cooked over an open fire; especially a whole animal carcass roasted on a spit	a restaurant where food is cooked on a grill
meat that has been barbecued or grilled in a highly seasoned sauce

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