Australian vs Commonwealth of Australia

Australian and Commonwealth of Australia both are nouns.

Word	Noun	Adjective	Verb	Adverb
Australian	Yes	Yes	No	No
Commonwealth of Australia	Yes	No	No	No

Australian (noun)	Commonwealth of Australia (noun)
the Austronesian languages spoken by Australian aborigines	a nation occupying the whole of the Australian continent; Aboriginal tribes are thought to have migrated from southeastern Asia 20,000 years ago; first Europeans were British convicts sent there as a penal colony
a native or inhabitant of Australia

Australian (adjective)	Commonwealth of Australia (adjective)
of or relating to or characteristic of Australia or its inhabitants or its languages