helmet vs headgear

helmet and headgear both are nouns.

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

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

Other hypernyms of helmet include headdress.

helmet (noun)	headgear (noun)
a protective headgear made of hard material to resist blows	clothing for the head
armor plate that protects the head	stable gear consisting of any part of a harness that fits about the horse's head
	the hoist at the pithead of a mine