Does that mean Australia is not the biggest island

Are continents islands?

The Australia thing is something we were taught in high school.

I think I remember being told Greenland was the largest island, while Australia was a continent

Something to do with tectonic plates

Continents is a human made construct that’s later rationalized with tectonic plates and other criteria. Basically, people around the Mediterranean Sea divided the Mediterranean Coast into 3 parts and later extended this concept.