Canberra vs Australian capital

Canberra and Australian capital both are nouns.

Word	Noun	Adjective	Verb	Adverb
Canberra	Yes	No	No	No
Australian capital	Yes	No	No	No

As nouns, Canberra and Australian capital are synonyms defined as:

Canberra and Australian capital: the capital of Australia; located in southeastern Australia

Other synonyms of Canberra include capital of Australia.

Canberra (noun)	Australian capital (noun)
the capital of Australia; located in southeastern Australia	the capital of Australia; located in southeastern Australia