What is the difference between a continent and an island?

I was intrigued by this question and did some research for myself, too.  A review of several geography books, including Geography for Dummies, not a very flattering title, and Don't Know Much About Geography, by Kenneth C. Davies, as well as several websites, left me quite dissatisfied.

What I have learned is that a continent is a large land mass surrounded by water.  Any land mass not large enough to be considered a continent is an island.  Hmmm.... What does that mean?  There are no scientific criteria whatsoever.  We cannot say that anything over X number of square miles is a continent and anything under X square miles is an island.  There are no geographical features involved except for the requirement of a land mass, which is required for both. 

I did learn that in the ancient world, there were three landmasses considered to be continents, which were Europe, Asia, and Africa (Davies).  But even though we have discovered the other four, I am not sure our geographic concept of this distinction is any less primitive than that of the ancient world!