My ten year old asked me to explain the Canadian system of government. I started out pretty confidently. Then I realized I have no clue... They are independent, but they are part of the Commonwealth. They have a queen... And Wikipedia is no help at all!
Both Canada and Australia are federations: therefore, besides the Crown in Right of Canada and the Crown in Right of the Commonwealth of Australia, there are Crowns in Right of each Canadian province and each Australian state. For example, there is the Crown in Right of the Province of British Columbia. The rights which the Crown possesses in right of a Canadian province are exercised by the province's lieutenant-governor (e.g., the Lieutenant-Governor of British Columbia), not the Governor-General of Canada, and such rights are exercised under the advice of the provincial ministers (not the federal ministers). The situation in Australia is analogous with governors and state ministers instead of the Canadian equivalents.