hearthrug vs rug

hearthrug and rug both are nouns.

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

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

hearthrug: a rug spread out in front of a fireplace
rug: floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)

Other hypernyms of hearthrug include carpet, carpeting.

hearthrug (noun)	rug (noun)
a rug spread out in front of a fireplace	floor covering consisting of a piece of thick heavy fabric (usually with nap or pile)