backrest vs ladder-back

backrest and ladder-back both are nouns.

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

As nouns, ladder-back is a hyponym of backrest; that is, ladder-back is a word with a more specific, narrower meaning than backrest:

backrest: a support that you can lean against while sitting
ladder-back: the backrest of a chair that consists of two uprights with connecting slats

Other hyponyms of backrest include cantle.

backrest (noun)	ladder-back (noun)
a support that you can lean against while sitting	the backrest of a chair that consists of two uprights with connecting slats
	a chair with a ladder-back