headgear vs chapeau

headgear and chapeau both are nouns.

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

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

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

headgear (noun)	chapeau (noun)
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