cookery vs grilling

cookery and grilling both are nouns.

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

As nouns, grilling is a hyponym of cookery; that is, grilling is a word with a more specific, narrower meaning than cookery:

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

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