Graeme, what you're looking for is not quite what you're expecting. The primary division is between "holy" magic, which is granted by a supernatural being, and "arcane" magic, which is directly controlled by the practitioner. "Holy" magic is then divided into alliance, neutral, and anarch, according to the position of the one granting it relative to the Creator.
John, all religious persons do have a skill in holy magic--they have a skill called Religion M1@0, and it bonuses their ability to perform other holy magic skills. It might not be on your sheet, because you did not list yourself a "professional" believer when we created your character and you've not attempted to pray or call on God (of which I am aware) since your character started play. As soon as you do that, I'll be asking you about your "religion".
Whether faith is "magic" is, I think, a semantic question--that is, it depends entirely on how you define "magic". My definition of "magic" is "power from outside the natural world". That distinguishes it from the psionic power that comes from within ourselves, the technological power that comes from the laws of physics and chemistry, and the physical power that comes from our biology (which one could argue is one of the others, but for the game it works much better to identify it as separate). It also means that if God does it, it is by this definition magic--and that hurricanes and earthquakes are not, in that sense, "acts of God".
Your character does not have to agree with this definition; he can believe that calling on God for help is not "magic", but something very different from "magic", and that can work for him.
My problem, as a game designer, is that I need a mechanic for "calling on God". Bear with me here.
I think you and I would agree (whatever anyone else on this board thinks) that God can and does heal people in response to prayer; I think we would also agree (again, without wishing an argument on the subject) that He does not always do so. There are uncounted prayers that God answers, and uncounted prayers that He seems not to answer, or at least, not in the terms we wished or expected.
Thus, quite apart from whether or not it should be called "magic", I face the problem of how to determine what happens. On the one hand, it would be entirely unrealistic (and terribly not fun) if every time you prayed something it happened immediately and exactly as stated; on the other hand, it would also be unfair and unrealistic for prayers never to be answered. Thus the answer provided by Multiverser (and some other but not all role playing games) is to let the dice decide, based on probabilities. Those probabilities are in turn based on your faith--as represented by your Religion skill--plus the numbers used to determine your chance of performing magic, because whatever else you want to argue, both are about introducing supernatural power into the natural world and directing it. A scale of difficulty is included, based on bias, so that it's easier to pray for simple blessings than to call lightning or fire from heaven, and that same bias system makes some things impossible in some worlds--consider it God's limitation on Himself in that world, that He has created lines He will not cross.
You don't have to believe that faith and magic are related to play the game; you just have to accept that in the mechanics, they are related.
I hope this helps.
--M. J. Young