headgear vs saddlery

headgear and saddlery both are nouns.

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

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

headgear: stable gear consisting of any part of a harness that fits about the horse's head
saddlery: gear for a horse

Other hypernyms of headgear include stable gear, tack.

headgear (noun)	saddlery (noun)
clothing for the head	gear for a horse
stable gear consisting of any part of a harness that fits about the horse's head	workshop where a saddler works
the hoist at the pithead of a mine