The following summary, prepared by Michael Goodwin in 2000 and recorded at
http://mcgoodwin.net/pages/gungermsteel.html. answers the question well. He indicates that the people came originally from mainland China. He also explains the language differences and similarities.
The islands of the Pacific were colonized by waves of colonists from Asia, arriving in New Guinea c. 40,000 BC (these became the New Guinea Highlanders and prob. the Philippine Negritos). The Austronesian migrations began from the Chinese mainland, reaching Taiwan first c. 3500 BC, the Philippines by 3000 BC, Sumatra and Java by 2000 BC, Northern New Guinea by 1600 BC, Samoa by 1200 BC, Hawaii, Easter Island, and Madagascar by 500 AD, etc. These Austronesian migrants became the Polynesians. The Austronesian languages include the Western Malayo-Polynesian (WMP) subfamily and Central-Eastern MP family including Oceanic. The double-outrigger sailing canoe made the Austronesian migration possible. Evidence of this spread comes from the characteristic artifacts (red pottery of Ta-p'en-k'eng style and subsequently the "tattooed" Lapita type of pottery, pigs, chickens, dogs, food production, seafaring, seafood, etc.) as well as analysis of the putative Proto-Austronesian language. They displaced less capable peoples but not the central or southern New Guineans, over whom they had no competitive advantage, and they had difficulty establishing themselves in W. and N. Australia (the languages there are not Austronesian).