snow gum vs eucalyptus tree

snow gum and eucalyptus tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
snow gum	Yes	No	No	No
eucalyptus tree	Yes	No	No	No

As nouns, eucalyptus tree is a hypernym of snow gum; that is, eucalyptus tree is a word with a broader meaning than snow gum:

snow gum: small to medium-sized tree of Australia and Tasmania having smooth white to light-grey bark shedding in patches or strips
eucalyptus tree: a tree of the genus Eucalyptus

Other hypernyms of snow gum include eucalypt, eucalyptus.

snow gum (noun)	eucalyptus tree (noun)
small to medium-sized tree of Australia and Tasmania having smooth white to light-grey bark shedding in patches or strips	a tree of the genus Eucalyptus