doggy bag vs paper bag

doggy bag and paper bag both are nouns.

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

As nouns, paper bag is a hypernym of doggy bag; that is, paper 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
paper bag: a bag made of paper or plastic for holding customer's purchases

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

doggy bag (noun)	paper 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