cherry birch vs birch tree

cherry birch and birch tree both are nouns.

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

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

cherry birch: common birch of the eastern United States having spicy brown bark yielding a volatile oil and hard dark wood used for furniture
birch tree: any betulaceous tree or shrub of the genus Betula having a thin peeling bark

Other hypernyms of cherry birch include birch.

cherry birch (noun)	birch tree (noun)
common birch of the eastern United States having spicy brown bark yielding a volatile oil and hard dark wood used for furniture	any betulaceous tree or shrub of the genus Betula having a thin peeling bark