Commonwealth of Australia vs Australian

Commonwealth of Australia and Australian both are nouns.

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

Commonwealth of Australia (noun)	Australian (noun)
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	the Austronesian languages spoken by Australian aborigines
	a native or inhabitant of Australia

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