Not that I think I have the definitive answer on this question, but:

Suppose I'm writing a reasonably long paper, broken up into sections. I use Lemmas for technical statements and so on, as many other answerers do. I would rather use Propositions, however, when the result is more global in scale: if it's going to be used outside its section, for example, I'll call it a Proposition, but if it's only used to build up things inside its own section I'll call it a Lemma. Then the Theorems are the statements I want people to take away from the paper.

In this paradigm, a Proposition is more like a Super-Lemma than a Mini-Theorem. I doubt that's a universal sentiment - probably it's not even universal among my own papers....