I am making a quiz and I want to know whether Australia or Oceania is the continent? I have searched it on Google but I can't find an answer.
Australia is a continent and Oceania is a region.
Continents are vaguely defined as large landmasses separated by water or just by historical context. Earth scientists have much more precise definitions of what a continental plate is vs an oceanic plate.
In the case of Australia, the continental plate consists of the landmasses Australia, Tasmania and New Guinea. Sometimes other names are used to clarify the difference between the country Australia and the continent.
Oceania is the region of island nations and sometimes Australia, located in or near the Pacific Ocean. There are a number of different definitions depending on the context. Usually Oceania includes islands that have no affiliation with the Australian continent.
A personal comment inspired by aretxabaleta's different, but also correct answer: Exact definitions can be difficult and often misleading as we tend to use language to label objects rather than processes, whiles Earth is better understood as processes, scientifically and socially.
Partly, it depends on where you got educated. In many countries of Europe, Oceania is the continent. Calling the continent Australia is pretty much considered "English-centric". The reasoning for calling it Oceania is that Australia is only part of the continent. The extend of the mainland during the ice ages included part of today's Indonesia and Papua-New Guinea. While calling it Australia makes some sense and it is the largest part of the continent, in a sense it is like if we were to call Asia, Russia.
Source: Wikipedia (Maximilian Dörrbecker (Chumwa) - Self made, using this map for the background, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=7382691)
This is Oceania according to this Norwegian meteorological website https://www.yr.no/place/Oceania/. As you can see, it is a quite a large area. The website has a very precise weather forecast for almost every place on Earth. The continent is Australia and the area of the Earth is Oceania.