back street vs alley

back street and alley both are nouns.

Word	Noun	Adjective	Verb	Adverb
back street	Yes	No	No	No
alley	Yes	No	No	No

As nouns, back street and alley are synonyms defined as:

Other synonyms of back street include alleyway.

back street (noun)	alley (noun)
a narrow street with walls on both sides	a narrow street with walls on both sides
	a lane down which a bowling ball is rolled toward pins