What is the difference between an island and a continent?

An island is a landmass surrounded by water, and by that definition Australia qualifies, as does every continent except the connected mass of Europe, Asia, and Africa. The distinction between island and continent is conventional rather than scientific, and the usual reasoning combines several factors: size, whether the landmass sits on its own continental crust and tectonic plate, distinctive geology, and distinctive flora, fauna, and human culture. Australia is treated as a continent because it satisfies all of those, sitting on its own plate with an isolated evolutionary history. Greenland, roughly a third of Australia's size, sits on the North American plate and is conventionally an island.

The awkwardness is visible in other cases. Zealandia, a largely submerged continental mass around New Zealand, satisfies the geological criteria for a continent while being about 94 percent underwater, and geologists have formally described it as such while it plays no role in the popular seven-continent scheme. India sits on its own tectonic plate and is called a subcontinent. The boundary between Europe and Asia runs approximately along the Urals by convention, with no physical division at all.

The practical answer is that these are categories built by people for describing the world, refined over centuries and never standardized by any international body, which is why the number of continents taught varies by country. That does not make them useless: they encode real distinctions in geology, biology, and human history. It does mean that arguments about whether a particular landmass qualifies are arguments about definitions rather than about facts, and the productive version asks which criterion you are applying rather than which answer is correct.