Unfortunately, they have been given real power with the Divine Rank mechanic in the SRD. I was never a fan of statting gods, but I guess if someone wants to play divine-epic-exalted style games, you need this.
No, I'm not talking about statting gods...something I find kinda cheesy myself. (For the record, if you encounter a god with book stats in my campaign, you're meeting a manifestation, an avatar, not the god itself.)
I'm just saying that in a reality in which there are beings called "gods" and they have "powers beyond the ken of mortal men" (in other words, a typical fantasy setting), there probably would be a discernable difference between what could be accomplished by divine and arcane magic, and in the methodologies by which such things could be accomplished.
As the old joke goes, when a scientist challenged God to a contest on creating life, the scientist said, "First we take some dirt..." and God interrupts "Ah-ah-aaaah!
Make your own dirt!"
As for the Priest description under the Magister heading (with which I'm quite familiar), I see it as either 1) a distinction without a difference- something I abhor, or possibly 2) the description of someone who is deluding themselves and/or others (see below).
In a sense, the gods of AU/AE are merely mythical- all power derives from the same source, despite what people believe.
Look at it this way: as much magic as there is in AU/AE (or most FRPGs), spellcasters would be quite aware as to the source of their powers. If that source were believed to be divine, ascertaining its divinity (or lack thereof) would be possible, if only by Akashics:
Memory Possession
The akashic can absorb the memories of any intelligent creature who is alive or who as ever lived for 1 round per level...Akashics use this ability to allow their allies to speak with and ask questions fo the possessing memory... AU p29
If there was no divinity, those who claimed there was would be naught but frauds. If there were, we get back to the distinction between arcane and divine as discussed above.
Unless, of course, the gods have fallen or have been diminished. Then, and only then, do we get into a quasi-Clarksian state in which "any arcane magic, sufficiently sophisticated, is indistinguishable from divine magic."