Answer:
The Māori are the indigenous people of New Zealand.
There are no grounds for dispute. The Moriori are Maori who inhabit the Chatham Islands just off New Zealand's South Island's east coast. There are some claims that the Moriori were first on the mainalnd, but there does not seem to be any evidence to support this claim. Despite having been scientifically debunked for nearly a century, the anti-Maori "Moriori myth" is still disseminated as racist propaganda whose purpose is to deny Maori rights and status as the original inhabitants of Aotearoa New Zealand.
See the related links for further information about the indigenous people of New Zealand.