river birch vs birch tree

river birch and birch tree both are nouns.

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

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

river birch: birch of swamps and river bottoms throughout the eastern United States having reddish-brown bark
birch tree: any betulaceous tree or shrub of the genus Betula having a thin peeling bark

Other hypernyms of river birch include birch.

river birch (noun)	birch tree (noun)
birch of swamps and river bottoms throughout the eastern United States having reddish-brown bark	any betulaceous tree or shrub of the genus Betula having a thin peeling bark