back country vs backwoods

back country and backwoods both are nouns.

Word	Noun	Adjective	Verb	Adverb
back country	Yes	No	No	No
backwoods	Yes	No	No	No

As nouns, back country and backwoods are synonyms defined as:

Other synonyms of back country include boondocks, hinterland.

back country (noun)	backwoods (noun)
a remote and undeveloped area	a remote and undeveloped area