eucalyptus vs red gum

eucalyptus and red gum both are nouns.

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

As nouns, red gum is a hyponym of eucalyptus; that is, red gum is a word with a more specific, narrower meaning than eucalyptus:

eucalyptus (noun)	red gum (noun)
a tree of the genus Eucalyptus	red gum tree of Tasmania
wood of any of various eucalyptus trees valued as timber	very large red gum tree
	a North American tree of the genus Liquidambar having prickly spherical fruit clusters and fragrant sap
	reddish-brown wood and lumber from heartwood of the sweet gum tree used to make furniture
	reddish-brown dried gummy exudation from any of several trees of the genus Eucalyptus especially Eucalyptus camaldulensis