gray birch vs birch tree

gray birch and birch tree both are nouns.

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

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

gray birch: medium-sized birch of eastern North America having white or pale grey bark and valueless wood; occurs often as a second-growth forest tree
birch tree: any betulaceous tree or shrub of the genus Betula having a thin peeling bark

Other hypernyms of gray birch include birch.

gray birch (noun)	birch tree (noun)
medium-sized birch of eastern North America having white or pale grey bark and valueless wood; occurs often as a second-growth forest tree	any betulaceous tree or shrub of the genus Betula having a thin peeling bark