Difference between "theorem" and "theory"

What is the difference between a theorem and a theory? The two words seem to be used to describe very similar things, but yet do not seem to be interchangeable.

For example, we have Pythagoras' theorem and Einstein's theory of relativity.

A theorem is a result that can be proven to be true from a set of axioms. The term is used especially in mathematics where the axioms are those of mathematical logic and the systems in question.

A theory is a set of ideas used to explain why something is true, or a set of rules on which a subject is based on.

I found a discussion where people were talking about the same matter, and someone put the difference between "theorem" and "theory" in a nutshell:

Theory - Verifiable Explanation.
Theorem - Demonstrable Explanation.

and explained:

Verifiable will mean that you can show that there is evidence for it. Demonstrable means that you can do it again to show people the evidence, and that they can do it too.

Wikipedia puts forth further differences:

The concept of a theorem is therefore fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical

"Empirical" means, "The word empirical denotes information gained by means of observation or experiments", whereas "deductively" means more of drawing from logic and reason, not facts.