shag rug vs rug

shag rug and rug both are nouns.

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

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

shag rug: a rug with long pile
rug: floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)

Other hypernyms of shag rug include carpet, carpeting.

shag rug (noun)	rug (noun)
a rug with long pile	floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)