wild plum vs plum tree

wild plum and plum tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
wild plum	Yes	No	No	No
plum tree	Yes	No	No	No

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

wild plum: an uncultivated plum tree or shrub
plum tree: any of several trees producing edible oval fruit having a smooth skin and a single hard stone

Other hypernyms of wild plum include plum.

wild plum (noun)	plum tree (noun)
fruit of the wild plum of southern United States	any of several trees producing edible oval fruit having a smooth skin and a single hard stone
an uncultivated plum tree or shrub