In mathematical writing, the word "Proposition" is often used to label lesser theorems. However, I tend to feel that there's a further difference in the way the words "Proposition" and "Theorem" are used. Namely that when a writer says: "Proposition. foo," I tend to feel that the writer is meaning "I propose that foo" or "I claim that foo holds." Whereas when a writer says "Theorem. foo," I tend to feel that this merely means "foo" or "foo holds."
Question (addressed especially to people who have written mathematical papers using these terms.) Would it be fair to say that you tend to use the words "Proposition" and "Theorem" differently, that this difference goes beyond merely a difference in the size or importance of the result being stated, and that you use the word "Proposition" to emphasize that you're actually claiming something, as opposed to merely stating its truth?