Commonwealth of Australia vs Western Australia

Commonwealth of Australia and Western Australia both are nouns.

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

Commonwealth of Australia (noun)	Western Australia (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	a state containing the western third of Australia