The aboriginal peoples are so different because they represent two got to the antipodes in two very separate migrations. The aboriginal people of Australia were the descendants of a migrant group that left Africa around 60,00 years ago. This group more or less followed the coast line along India and Indochina before reaching New Guinea, which was connected to Australia by a land bridge at the time. There is still some debate as to the where and when the Indigenous Australians came from but the above seems to be the modern consensus due to recent work tracing genotypes.
The Maori people of New Zealand are a pacific Island people, sharing large elements of their language and culture with the other pacific Island peoples. They were the final part of the Polynesian colonization of the pacific, reaching New Zealand from the Cook Islands around 800 years ago.
As far as I know there was no interaction between the two people before the arrival of Europeans.
http://en.wikipedia.org/wiki/History_of_Indigenous_Australians
It is important to remember that, despite how it looks on a map, New Zealand and Australia are not actually that close to one another. There is over 2000km of sea between the two nations, meaning that travel between them was effectively impossible for the two indigenous groups.
/u/DeepSpawn has explained why they're so different, so I'll just answer your second question.
There is no evidence or recorded interactions between Māori and Australian Aborigines prior to the arrival of Europeans in New Zealand -- it is believed that the first Māori travelled to Australia in trading ships from the late 1700s. Even then, Māori chiefs traded with Europeans in Australia. This picture from 1823 shows Māori chiefs standing in a Sydney garden.
Interestingly (and tangential to your question, but I always find this fascinating when talking about Māori-Aborigine relations), Māori in Australia were historically considered "white" and Māori Australian residents actually had the right to vote in Australia before Aborigines did.