downstairs vs down the stairs

downstairs is an adjective but down the stairs is not an adjective.

Word	Noun	Adjective	Verb	Adverb
downstairs	No	Yes	No	Yes
down the stairs	No	No	No	Yes

As adverbs, downstairs and down the stairs are synonyms defined as:

Other synonyms of downstairs include below, on a lower floor.

downstairs (adjective)	down the stairs (adjective)
on or of lower floors of a building

downstairs (adverb)	down the stairs (adverb)
on a floor below	on a floor below