Well, I'm not sure if this helps or not, but if you think about, some of the symbols would be troublesome in certain branches of mathematics. The most related example is the vertical bar which represents "such that." In number theory, we use a vertical bar to represent divisbility. Wouldn't it make things more difficult and confusing if we used the same symbol to mean different things? Also, as I'm sure we are all coming to realize, every greek letter seems to have a function as well, so the backwards c with a line through it is probably a function in some subject.

I also used to wonder about the differences between lemmas/theorems/etc. Here's a couple more:

Axiom - self-eveident truth that requires no proof (I can think of a couple teachers who would disagree with that) / universally accepted rule or principle.

Theorem - a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas.

Formula - a rule or principle, frequently expressed in algebraic symbols.

Rule - A determinate method prescribed for performing any operation and producing a certain result.

Principle - a fundamental, primary, or general law or truth from which others are derived.

(I suppose the last couple are a bit silly, but it's good to have clear definitions for things, isn't it?)