flying carpet vs rug

flying carpet and rug both are nouns.

Word	Noun	Adjective	Verb	Adverb
flying carpet	Yes	No	No	No
rug	Yes	No	No	No

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

flying carpet: (Asian folktale) an imaginary carpet that will fly people anywhere they wish to go
rug: floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)

Other hypernyms of flying carpet include carpet, carpeting.

flying carpet (noun)	rug (noun)
(Asian folktale) an imaginary carpet that will fly people anywhere they wish to go	floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)