mitre vs headgear

mitre and headgear both are nouns.

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

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

Other hypernyms of mitre include headdress.

mitre (noun)	headgear (noun)
a liturgical headdress worn by bishops on formal occasions	clothing for the head
the surface of a beveled end of a piece where a miter joint is made	stable gear consisting of any part of a harness that fits about the horse's head
joint that forms a corner; usually both sides are bevelled at a 45-degree angle to form a 90-degree corner	the hoist at the pithead of a mine