European beech vs common beech

European beech and common beech both are nouns.

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

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

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

Other synonyms of European beech include Fagus sylvatica.

European beech (noun)	common 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