hard beech vs evergreen beech

hard beech and evergreen beech both are nouns.

Word	Noun	Adjective	Verb	Adverb
hard beech	Yes	No	No	No
evergreen beech	Yes	No	No	No

As nouns, evergreen beech is a hypernym of hard beech; that is, evergreen beech is a word with a broader meaning than hard beech:

hard beech: tall New Zealand tree yielding very hard wood
evergreen beech: any of various beeches of the Southern Hemisphere having small usually evergreen leaves

Other hypernyms of hard beech include southern beech.

hard beech (noun)	evergreen beech (noun)
tall New Zealand tree yielding very hard wood	any of various beeches of the Southern Hemisphere having small usually evergreen leaves