Australian citizenship is a completely separate subject to permanent residence or living in Australia and the two should not be confused. Many people who move to Australia never become Australian Citizens as travel on their original passport when they go overseas. It is optional to become an Australian Citizen, though permanent residence visa holders enjoy most of the same rights and privileges that Australian Citizens do. Though you cannot vote in State, Territory or Federal elections, you cannot apply for an Australian passport and you do not have access to Australian Consular assistance when you are outside Australia (as have to call on the country under which passport you are travelling.
You should also be aware that some countries can automatically revoke your citizenship if you become a citizen of Australia by naturalisation, so it is wise to check with your original country if you want to retain your citizenship before you apply to become an Australian citizen.
The citizenship process involves completing and lodging an application for citizenship form which can be completed online or by completing a paper application for yourself and any children included in your application. Once your form has been received by the Department of Immigration and Border Protection, you will be invited to attend a citizenship appointment which may include either a citizenship test or an interview (if you are not required to sit the test). The Department will notify you of their decision to grant citizenship and you must be in Australia at the time that the citizenship decision is made.
For more information and how to apply for Australian Citizenship, visit the Department of Immigration and Border Protection’s Citizenship Website.