paper bag vs doggie bag

paper bag and doggie bag both are nouns.

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

As nouns, doggie bag is a hyponym of paper bag; that is, doggie bag is a word with a more specific, narrower meaning than paper bag:

paper bag: a bag made of paper or plastic for holding customer's purchases
doggie 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

Other hyponyms of paper bag include doggy bag, grocery bag.

paper bag (noun)	doggie bag (noun)
a bag made of paper or plastic for holding customer's purchases	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