What is the difference between an island and continent?

Geographically speaking, continents are bigger than islands.

Geologically speaking, they are different in their rock density. Continents are made up of low-density rock, so they float high on Earth's molten mantle like big rafts. Ocean crust is denser, so it floats low on the mantle. Most islands are really extensions of the ocean floor - undersea volcanoes pump out dense lava that cools into ocean floor crust and sometimes piles up above sea level.

An example often quoted is that of Australia (a continent) and Greenland (an island). Geographically, Australia is a continent, not an island. As a landform, it could be considered an island as it is entirely surrounded by water and not joined onto any other land mass. For this reason, it is often referred to as an island continent. Australia is too big to be formally classified as an island. The world's largest island is actually Greenland.

Another reason why Australia is also considered a continent is because it sits on its own tectonic plate. This is different from Greenland, which uses the same land mass as North America. That is why the geological appearances are much different in Australia than anywhere else. A place like Greenland shares the same geologic attributes as North America.