headstall vs headpiece

headstall and headpiece both are nouns.

Word	Noun	Adjective	Verb	Adverb
headstall	Yes	No	No	No
headpiece	Yes	No	No	No

As nouns, headstall and headpiece are synonyms defined as:

headstall and headpiece: the band that is the part of a bridle that fits around a horse's head

headstall (noun)	headpiece (noun)
the band that is the part of a bridle that fits around a horse's head	a protective helmet for the head
	the band that is the part of a bridle that fits around a horse's head