common birch vs birch tree

common birch and birch tree both are nouns.

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

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

common birch: European birch with silvery white peeling bark and markedly drooping branches
birch tree: any betulaceous tree or shrub of the genus Betula having a thin peeling bark

Other hypernyms of common birch include birch.

common birch (noun)	birch tree (noun)
European birch with silvery white peeling bark and markedly drooping branches	any betulaceous tree or shrub of the genus Betula having a thin peeling bark