Theology and philosophy of religion: what are they?

So, a running commentary in the post bringing over the discussion from Butterflies and Wheels is about what is the difference between theology and philosophy of religion, and this morning I came up with an idea:

Theology is the study of theistic religion.

Philosophy of religion studies religion in general, without focusing on theistic religions.

This is brought to light by discussions of Buddism.  Is it a religion, or isn’t it?  It certainly is generally considered a religion, but recent arguments that say that a religion has to include a supernatural deity and so Buddism isn’t one.  And so this debate both highlights and will settle if there is any difference between theology and philosophy of religion:

If Buddism is a religion, then there will be no theological study of it — since it isn’t theistic — and philosophy of religion will cover it while theology will not.  Philosophy of religion, however, will cover it in addition to covering theistic religions (it’s a more general field than theology).

If it turns out that Buddism is not a religion because to be a religion you need a god, and that would mean that Buddism, which is not theistic, is not a religion, then there  is no difference in the subject matter of philosophy of religion and theology, and there shouldn’t be any difference in method either since both would simply choose the methods that best study theistic religions.

So, if we settle this question, we have our answer, no matter what traditionally has been done.