river red gum vs eucalyptus

river red gum and eucalyptus both are nouns.

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

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

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

Other hypernyms of river red gum include eucalypt, eucalyptus tree.

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