Although Australia and New Zealand are relatively close to one another, their geography is very different. This is mainly true of their physical geography.
In terms of human geography, the two countries are rather similar. Both countries were colonized by the United Kingdom. This has meant that they have very similar systems of government and cultures. They differ to some degree in their demographics but are both largely made up of people of European descent.
Physically, however, the countries are very different. New Zealand is made up of relatively small islands whose climate is affected by the ocean. Therefore, it has a mild marine west-coast climate. By contrast, Australia is a continent. This means that most of its climate is not controlled by the ocean. Australia does have a small zone of marine west-coast climate and some tropical areas, but the majority of its area is desert.
New Zealand is seismically active. It has many volcanic peaks as well as hot springs and geysers. It is very hilly and mountainous. By contrast, Australia is very seismically inactive. It is the flattest and lowest continent in the world.
Thus, these two countries are geographically very different.