paper birch vs birch tree

paper birch and birch tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
paper birch	Yes	No	No	No
birch tree	Yes	No	No	No

As nouns, birch tree is a hypernym of paper birch; that is, birch tree is a word with a broader meaning than paper birch:

paper birch: small American birch with peeling white bark often worked into e.g. baskets or toy canoes
birch tree: any betulaceous tree or shrub of the genus Betula having a thin peeling bark

Other hypernyms of paper birch include birch.

paper birch (noun)	birch tree (noun)
small American birch with peeling white bark often worked into e.g. baskets or toy canoes	any betulaceous tree or shrub of the genus Betula having a thin peeling bark