stair-carpet vs carpet

stair-carpet and carpet both are nouns.

Word	Noun	Adjective	Verb	Adverb
stair-carpet	Yes	No	No	No
carpet	Yes	No	Yes	No

As nouns, carpet is a hypernym of stair-carpet; that is, carpet is a word with a broader meaning than stair-carpet:

stair-carpet: a strip of carpet for laying on stairs
carpet: floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)

Other hypernyms of stair-carpet include carpeting, rug.

stair-carpet (noun)	carpet (noun)
a strip of carpet for laying on stairs	floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)
	a natural object that resembles or suggests a carpet

stair-carpet (verb)	carpet (verb)
	cover with a carpet
	cover completely, as if with a carpet
	form a carpet-like cover (over)