river gum vs eucalyptus tree

river gum and eucalyptus tree both are nouns.

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

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

river gum: somewhat crooked red gum tree growing chiefly along rivers; has durable reddish lumber used in heavy construction
eucalyptus tree: a tree of the genus Eucalyptus

Other hypernyms of river gum include eucalypt, eucalyptus.

river gum (noun)	eucalyptus tree (noun)
somewhat crooked red gum tree growing chiefly along rivers; has durable reddish lumber used in heavy construction	a tree of the genus Eucalyptus