My own interpretation of the workings of magic is that, while science will tell you the exact steps you need to get a particular result, and any person who follows those steps will always get exactly the same result, magic gives you things that are conceptually related to the idea of the effect you want to create. Perhaps on top of hard mechanics that tap into some universal power source, but those mechanics are never sufficient in and of themselves.
The bat guano of a fireball only works because of a conceptual association. You could transfer that association to, say, gunpowder, and it will still work if that association is still maintained (but won't work if the conceptual part is broken). Likewise, someone attempting to cast fireball with bat guano, but doesn't have a grasp of the association thereof, will not be able to cast the spell.
Essentially, that's the difference I see between science and magic. With science, what you believe doesn't matter; the universe will continue to behave the way it always has. A gun will always be a gun, no matter who shoots it. With magic, what you believe does matter, which is why it's difficult to transfer knowledge from one person to another, and why you have to study another wizard's magic book to figure out his spells. You have to not only understand the mechanics, but also the underlying conceptions and metaphysical associations, and then translate those to your own versions of each.