American elm vs elm tree

American elm and elm tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
American elm	Yes	No	No	No
elm tree	Yes	No	No	No

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

American elm: large ornamental tree with graceful gradually spreading branches common in eastern North America
elm tree: any of various trees of the genus Ulmus: important timber or shade trees

Other hypernyms of American elm include elm.

American elm (noun)	elm tree (noun)
large ornamental tree with graceful gradually spreading branches common in eastern North America	any of various trees of the genus Ulmus: important timber or shade trees