prayer rug vs rug

prayer rug and rug both are nouns.

Word	Noun	Adjective	Verb	Adverb
prayer rug	Yes	No	No	No
rug	Yes	No	No	No

As nouns, rug is a hypernym of prayer rug; that is, rug is a word with a broader meaning than prayer rug:

prayer rug: a small rug used by Muslims during their devotions
rug: floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)

Other hypernyms of prayer rug include carpet, carpeting.

prayer rug (noun)	rug (noun)
a small rug used by Muslims during their devotions	floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)