headgear vs hackamore

headgear and hackamore both are nouns.

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

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

headgear: stable gear consisting of any part of a harness that fits about the horse's head
hackamore: rope or canvas headgear for a horse, with a rope for leading

Other hyponyms of headgear include bridle, halter.

headgear (noun)	hackamore (noun)
clothing for the head	rope or canvas headgear for a horse, with a rope for leading
stable gear consisting of any part of a harness that fits about the horse's head
the hoist at the pithead of a mine