backstairs vs stairway

backstairs and stairway both are nouns.

Word	Noun	Adjective	Verb	Adverb
backstairs	Yes	Yes	No	No
stairway	Yes	No	No	No

As nouns, stairway is a hypernym of backstairs; that is, stairway is a word with a broader meaning than backstairs:

backstairs: a second staircase at the rear of a building
stairway: a way of access (upward and downward) consisting of a set of steps

Other hypernyms of backstairs include staircase.

backstairs (noun)	stairway (noun)
a second staircase at the rear of a building	a way of access (upward and downward) consisting of a set of steps

backstairs (adjective)	stairway (adjective)
secret and sly or sordid