grocery bag vs carrier bag

grocery bag and carrier bag both are nouns.

Word	Noun	Adjective	Verb	Adverb
grocery bag	Yes	No	No	No
carrier bag	Yes	No	No	No

As nouns, carrier bag is a hypernym of grocery bag; that is, carrier bag is a word with a broader meaning than grocery bag:

grocery bag: a sack for holding customer's groceries
carrier bag: a bag made of paper or plastic for holding customer's purchases

Other hypernyms of grocery bag include paper bag, poke, sack.

grocery bag (noun)	carrier bag (noun)
a sack for holding customer's groceries	a bag made of paper or plastic for holding customer's purchases