ladder-back chair vs ladder-back

ladder-back chair and ladder-back both are nouns.

Word	Noun	Adjective	Verb	Adverb
ladder-back chair	Yes	No	No	No
ladder-back	Yes	No	No	No

As nouns, ladder-back chair and ladder-back are synonyms defined as:

ladder-back chair (noun)	ladder-back (noun)
a chair with a ladder-back	the backrest of a chair that consists of two uprights with connecting slats
	a chair with a ladder-back