cooking vs culinary art

cooking and culinary art both are nouns.

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

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

cooking: 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

cooking (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