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Depends on the source material, some make priests just be a "divine mage" of sorts, some make priests be something entirelly disconnected from mages and their magic.
In general, as far as I've seen, priests make miracles through divine power(blessings and such) while mages do the impossible through their own power(and/or the knowledge they acquire through their studies which expands their consciousness and ability to perceive reality and thus directly influence it).
I may conside priests as casters like mages, but in general I don't see them as the same thing.