What is evolution a theory of?

Real quick for the biologists in the house.  I want to pare this question down to the minimum so that maybe someone shows me where I'm going wrong.

People claim to believe in something they call the theory of natural selection by differential reproduction.  What does this theory purport to explain?

Does it explain the origin of life?  No, it takes reproduction as one of its premises, so it can't be expected to explain that.

Does it explain species we find on earth today?  Well, yes, insofar as it contends that current species are produced by modifications of old species.  However, it really only explains the selection of new species, and not their production, per se.  It says that species that are more adapted to their environment will reproduce better, and so selection will assure us that these are the ones we find later on.  But then it measures how adapted an animal is by how well it reproduces, which leaves you with a tautology, not a theory.  I guess there is some amount of content to claiming that the things we see are around because they are good at making copies of themselves.  You could imagine a world populated primarily by things that lasted a really long time individually, and not by things that reproduce at all.  But do we really take evolution to be a theory that primarily says that it's really hard to keep existing without making a copy of yourself?

Does it explain how new species arise or explain the diversity of life?  Not at all.  It says that there will be lots of copies of things that reproduce more.  When you ask why something started reproducing more, they tell you that it's because of better adaptation.  When you leave aside the tautological question above and just ask, well, how did it get better adapted, you are told that it was a chance mutation.  Sometimes you get a slightly ore sophisticated answer about a chance mutation that improved its adaptability or ability to learn, but in the end, the answer to the question of why is the biological world so diverse seem to boil down to "chance".  But chance is explicitly outside of the theory.  The theory talks about how you end up with more or less of what already exists.  No matter how slow you imagine change to happen, you still have to invoke some change to get anywhere at all, and it still inherently falls outside of the theory which deals only in similarity.  You will recall how Zeno proved movement was impossible.  

So if evolution is not a theory of any of these things, then what exactly is it a theory of, pray tell?  

It seems we need a theory of chance.  A theory of difference instead of reproduction.