Australia has 3x the land area as Greenland so the line is probably somewhere in between there.
Europe, Asia, and Africa are names people gave to the major regions surrounding the Mediterranean long ago. Later generations generalized the idea. First by using the same names for lands far behind the Europe, Asia, and Africa they were familiar with, and later by giving new names to separate landmasses. Whatever a continent is, Europe, Asia, and Africa are continents.
The main difference between a sea and a lake is that a sea is a part of the ocean. The Black Sea and the Baltic Sea are seas, while the Caspian Sea and the Great Lakes are lakes. The Caribbean Sea and the Sargasso Sea have names because people needed names for those regions. And because they consist of water connected to the ocean, calling them seas seemed appropriate.
I think it might be considered a continent because people were looking for a continent. Since Roman times, there was reputed to be a continent at the South Pole called Terra Australis. Captain Cook was looking for Terra Australis, but found Australia instead. They new they weren't at the South Pole, but they decided to call the place Australia anyway (Antarctica would not be seen until several decades later.) I suspect the continent classification was cast as soon as they started calling the place Australia.
It's certainly arbitrary that the Gulf of Mexico isn't considered a sea. (or various other "parts of the ocean" referred to as "gulfs" or "bays")
"The main difference between a sea and a lake is that a sea is a part of the ocean."
Ok, so you have decided that the Caspian Sea isn't actually a sea? Well I guess all bets are off if you can do that.... :)