cooking vs frying

cooking and frying both are nouns.

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

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

cooking: the act of preparing something (as food) by the application of heat
frying: cooking in fat or oil in a pan or griddle

cooking (noun)	frying (noun)
the act of preparing something (as food) by the application of heat	cooking in fat or oil in a pan or griddle