hat vs headgear

hat and headgear both are nouns.

Word	Noun	Adjective	Verb	Adverb
hat	Yes	No	Yes	No
headgear	Yes	No	No	No

As nouns, headgear is a hypernym of hat; that is, headgear is a word with a broader meaning than hat:

hat: headdress that protects the head from bad weather; has shaped crown and usually a brim
headgear: clothing for the head

Other hypernyms of hat include headdress.

hat (noun)	headgear (noun)
an informal term for a person's role	clothing for the head
headdress that protects the head from bad weather; has shaped crown and usually a brim	stable gear consisting of any part of a harness that fits about the horse's head
	the hoist at the pithead of a mine

hat (verb)	headgear (verb)
put on or wear a hat
furnish with a hat