smooth-leaved elm vs elm tree

smooth-leaved elm and elm tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
smooth-leaved elm	Yes	No	No	No
elm tree	Yes	No	No	No

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

smooth-leaved elm: European elm with lustrous smooth leaves used as an ornamental
elm tree: any of various trees of the genus Ulmus: important timber or shade trees

Other hypernyms of smooth-leaved elm include elm.

smooth-leaved elm (noun)	elm tree (noun)
European elm with lustrous smooth leaves used as an ornamental	any of various trees of the genus Ulmus: important timber or shade trees