common beech vs European beech

common beech and European beech both are nouns.

Word	Noun	Adjective	Verb	Adverb
common beech	Yes	No	No	No
European beech	Yes	No	No	No

As nouns, common beech and European beech are synonyms defined as:

common beech and European beech: large European beech with minutely-toothed leaves; widely planted as an ornamental in North America

Other synonyms of common beech include Fagus sylvatica.

common beech (noun)	European beech (noun)
large European beech with minutely-toothed leaves; widely planted as an ornamental in North America	large European beech with minutely-toothed leaves; widely planted as an ornamental in North America