white ash vs eucalyptus

white ash and eucalyptus both are nouns.

Word	Noun	Adjective	Verb	Adverb
white ash	Yes	No	No	No
eucalyptus	Yes	No	No	No

As nouns, eucalyptus is a hypernym of white ash; that is, eucalyptus is a word with a broader meaning than white ash:

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

Other hypernyms of white ash include eucalypt, eucalyptus tree.

white ash (noun)	eucalyptus (noun)
spreading American ash with leaves pale green or silvery beneath and having hard brownish wood	a tree of the genus Eucalyptus
small to medium-sized tree of Australia and Tasmania having smooth white to light-grey bark shedding in patches or strips	wood of any of various eucalyptus trees valued as timber