cookery vs culinary art

cookery and culinary art both are nouns.

Word	Noun	Adjective	Verb	Adverb
cookery	Yes	No	No	No
culinary art	Yes	No	No	No

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

cookery: the act of preparing something (as food) by the application of heat
culinary art: the practice or manner of preparing food or the food so prepared

cookery (noun)	culinary art (noun)
the act of preparing something (as food) by the application of heat	the practice or manner of preparing food or the food so prepared