In researching tiki, I realized that these terms are often used interchangeably and I wanted to know the difference.
Oceania: The largest region of Pacific islands including Australia: Australasia, Melanesia, Micronesia and Polynesia, extends all the way to Hawaii. When I visited the Bishop Museum in Honolulu they had great displays on the history of migration of peoples from Asia through to all of these regions. Link
Polynesia: Subregion of Oceania, made up of more than 1,000 islands scattered over the central and southern Pacific Ocean. New Zealand is in the region too. Link
South Pacific: Just the Pacific Ocean islands in the Southern Hemisphere