Commonwealth of Australia vs New South Wales

Commonwealth of Australia and New South Wales both are nouns.

Word	Noun	Adjective	Verb	Adverb
Commonwealth of Australia	Yes	No	No	No
New South Wales	Yes	No	No	No

Commonwealth of Australia (noun)	New South Wales (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	an Australian state in southeastern Australia