What is the difference between (probability) and (probability-theory)? If there is none, is it better to use both tags or to decide on one (by tossing a fair coin, of course)?
I view the "probability" tag for questions in which one wants a probability or expected value calculated. A classic example would be this one: If a 1 meter rope is cut at two uniformly randomly chosen points (to give three pieces), what is the average length of the smallest piece?
I view the "probability theory" tag for questions about, well, the theory of probability, such as a question about sigma-algebras, or how Lebesgue measure is used to define expectation, such as this one: Lebesgue integral basics.
Obviously there would be some overlap at the boundary between the two tags as I have defined them. A rough analogy would be the difference between the "calculus" and "real analysis" tags.
The user base currently seems to use these tags interchangeably rather than the way I have defined them. (In fact, the Lebesgue integral question is actually tagged "probability" rather than "probability theory.") But if people like my distinction we could codify it in the tag wikis, and then hopefully the user base would eventually converge to using these tags this way.
(While I would prefer this to be the solution, I don't feel strongly enough about it to argue too much if everyone else prefers to merge the two tags. I would also be interested to hear the opinions of the other people who are active in these two tags.)
Update: Since the community seems to be in support of this view, I have requested that these changes be made to the probability and probability-theory tag wikis, and these changes have been accepted. With respect to Willie Wong's comment, we'll have to see how well new question askers follow this convention.
Looking at these tags now 5 months later, it seems they're still quite thoroughly mixed up: probability-theory is full of basic questions about calculating expected values etc., while probability contains many advanced and theoretical questions that should probably go under -theory under Mike's convention.
So I'd like to revive this discussion: should we merge probability-theory into probability, or is this just a case of needing more aggressive retaggers?