Oceania is a name used in geography for the continent made up by Australia, New Zealand, New Guinea, and several other island nations in the surrounding area. Some people call this part of the world Australasia instead.
The term "Oceania" does not have one single agreed definition. In politics (United Nations etc) it includes Australia and the nations of the Pacific from Papua New Guinea east, but not the Malay Archipelago or Indonesian New Guinea.
The widest definition of Oceania includes the entire region between continental Asia and the Americas, including islands in the Pacific Rim such as the Japanese archipelago, Taiwan, and the Aleutian islands. On the other hand, the Oceania ecozone includes all of Micronesia, Fiji, and all of Polynesia except New Zealand.
For these reasons, it is not correct to say that Australasia is part of Oceania, because what is meant by 'Oceania' is not clear. Australasia has an exact definition in biogeography and geology. Australasia includes New Zealand, Australia (including Tasmania), and Melanesia, New Guinea, and the islands just north and east of Australia. All these are south-east of the Bali–Lombok line. This is known as the Wallace Line, after Alfred Russel Wallace.