doggy bag vs carrier bag

doggy bag and carrier bag both are nouns.

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

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

doggy bag: a bag for food that a customer did not eat at a restaurant; the transparent pretense is that the food is taken home to feed the customer's dog
carrier bag: a bag made of paper or plastic for holding customer's purchases

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

doggy bag (noun)	carrier bag (noun)
a bag for food that a customer did not eat at a restaurant; the transparent pretense is that the food is taken home to feed the customer's dog	a bag made of paper or plastic for holding customer's purchases