cedar elm vs elm tree

cedar elm and elm tree both are nouns.

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

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

cedar elm: elm of southern United States and Mexico having spreading pendulous corky branches
elm tree: any of various trees of the genus Ulmus: important timber or shade trees

Other hypernyms of cedar elm include elm.

cedar elm (noun)	elm tree (noun)
elm of southern United States and Mexico having spreading pendulous corky branches	any of various trees of the genus Ulmus: important timber or shade trees