American hazel vs hazelnut tree

American hazel and hazelnut tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
American hazel	Yes	No	No	No
hazelnut tree	Yes	No	No	No

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

American hazel: nut-bearing shrub of eastern North America
hazelnut tree: any of several shrubs or small trees of the genus Corylus bearing edible nuts enclosed in a leafy husk

Other hypernyms of American hazel include hazel, hazelnut.

American hazel (noun)	hazelnut tree (noun)
nut-bearing shrub of eastern North America	any of several shrubs or small trees of the genus Corylus bearing edible nuts enclosed in a leafy husk