New Zealand and Australia are not in the same continent, but they are usually grouped together using the term Australasia. This term is used mostly to refer to countries that are found within a particular geographical region under Oceania. Oceania is a geographical region on the Earth's surface that has a lot of islands.
Some parts of Australia and New Zealand belong to this region, and that is why they are classified together with other islands to form what is known as Australasia. By this explanation, you can easily figure out that Australasia is just a sub-region out of about three others that fall under Oceania. The remaining three sub-regions under Oceania are Polynesia, Micronesia, Melanesia.
Australasia is very close to the southern ocean by its south, the Indian Ocean by its west, and the Pacific Ocean by its East. At times, Australasia can be used as a continent; it is only referring to Australia, which is a continent on its own because New Zealand is not part of the continent.