There is a widely accepted difference between islands and continents in terms of geology. Continents are often considered to be the largest landmass of a particular continental plate; this holds true for Australia, which sits on its own continental lithosphere and tectonic plate (the Australian Plate).
By contrast, islands are usually seen as being extensions of the oceanic crust (e.g. volcanic islands), or as belonging to a continental plate containing a larger landmass (continental islands); the latter is the case of Greenland, which sits on the North American Plate.