ladder-back vs ladder-back chair

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

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

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

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