grilling vs cooking

grilling and cooking both are nouns.

Word	Noun	Adjective	Verb	Adverb
grilling	Yes	No	No	No
cooking	Yes	No	No	No

As nouns, cooking is a hypernym of grilling; that is, cooking is a word with a broader meaning than grilling:

grilling: cooking by direct exposure to radiant heat (as over a fire or under a grill)
cooking: the act of preparing something (as food) by the application of heat

Other hypernyms of grilling include cookery, preparation.

grilling (noun)	cooking (noun)
cooking by direct exposure to radiant heat (as over a fire or under a grill)	the act of preparing something (as food) by the application of heat