If Australia is a continent, what is Oceania?

And if Oceania is not a continent, what is New Zealand part of? Australia? Are they still liberal with citizenship between AUS and NZ (i.e. you can be legally emplyed in AUS if you are a NZ citizen)? And Australia is both a continent and a country, does it have states similar to the US? Or regions and citites? I feel so ignorant to the goings-on of that region of the Pacific, ever notice how it's pretty much the only place in the world we don't hear about in the news in the US? You don't need to answer that last one.