It's fuzzy rather than arbitrary, because the universe resists categorization. Australia is the dominant landmass on its tectonic plate, and it's relatively far away from other major landmasses. Greenland is a lesser landmass on the North American Plate, and it's much closer to the mainland.
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.