common birch vs European white birch

common birch and European white birch both are nouns.

Word	Noun	Adjective	Verb	Adverb
common birch	Yes	No	No	No
European white birch	Yes	No	No	No

As nouns, common birch and European white birch are synonyms defined as:

common birch and European white birch: European birch with silvery white peeling bark and markedly drooping branches

Other synonyms of common birch include Betula pendula, silver birch.

common birch (noun)	European white birch (noun)
European birch with silvery white peeling bark and markedly drooping branches	European birch with silvery white peeling bark and markedly drooping branches