TITLE: What is the difference between a proposition and a theorem?
QUESTION [27 upvotes]: What is the difference between a proposition and a theorem? How do people decide which of the two to use in, e.g., textbooks? 
Somehow I think "proposition" sounds less serious.

REPLY [2 votes]: Actually, according to the very good book Mathematics for Computer Science (by Eric Lehman and F Thomson Leighton), propositions and theorems are not the same (see page 7 and page 8).
Proposition is some statement (think of it as some verbally told/claimed expression), which (important point ->) can be either (1)True or (2)False.
Theorem is a Proposition which has passed the mathematical verification process and is proved to be True.
Note, that verification can be achieved in some different ways/strategies. E.g. induction, predicates, or etc.