omelet pan vs cooking pan

omelet pan and cooking pan both are nouns.

Word	Noun	Adjective	Verb	Adverb
omelet pan	Yes	No	No	No
cooking pan	Yes	No	No	No

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

Other hypernyms of omelet pan include pan.

omelet pan (noun)	cooking pan (noun)
pan for cooking omelets	cooking utensil consisting of a wide metal vessel