I learned (in our superior American public school system) that a continent is a land mass of a given size, and its surrounding islands of a smaller size. So now that North and South America are two different land masses, they qualify as being different. Europe and Asia, I think, were divided by some mountains. Eventually, somebody noticed that mountains aren't water, and started teaching us Eurasia, although the terms Europe and Asia are still favored these days outside of the classroom.