mountain ash vs ash tree

mountain ash and ash tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
mountain ash	Yes	No	No	No
ash tree	Yes	No	No	No

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

mountain ash: low-growing ash of Texas
ash tree: any of various deciduous pinnate-leaved ornamental or timber trees of the genus Fraxinus

Other hypernyms of mountain ash include ash.

mountain ash (noun)	ash tree (noun)
any of various trees of the genus Sorbus	any of various deciduous pinnate-leaved ornamental or timber trees of the genus Fraxinus
low-growing ash of Texas
tree having wood similar to the alpine ash; tallest tree in Australia and tallest hardwood in the world