Such things greatly depend on how much detail is actually hardwired into character classes within a given system.

In AD&D, a wizard is basically his spellbook and nothing else. 3rd Edition added feats to modify how the spells are cast, but it's still the spells that define the character. Skills don't seem to really make much of a difference.
Clerics don't have a lot more either. They have the ability to turn undead, which in lots of campaigns ends up mostly irrelevant, and can also use armor and hit better with weapons. But it's still primarily the spell list that sets them apart from wizards.
But then we also have psions, which supposedly are completely different, yet still are defined entirely by their power list. Which mostly does the same things as the wizard spell list.

In the Conan RPG, having priests being ordinary sorcerers with theolofical education makes a lot of sense. In that world gods are very distant, if they even exist at all. A few minor gods are known to exist with certainty, but those might also be called demons. Priests seem to be either charlatans, or well intentioned but possibly deluded about their gods. Using a single character class and having access to the same spells is a very obvious choice.
Dragon Age is an interesting case, as there are two types of priests that are shown. The human chanters and the elven keepers. The chanters follow the tradition of a prophet who led a great crusade against a nation ruled by evil wizards, and they consider all magic to be evil. They don't have any magic powers at all and are just ordinary people with no special abilities. The elven keepers are more like shamans and witch doctors who believe into a pantheon of gods, but don't claim to have any personal connection to them. Their power comes directly from the world of spirits. Their role as spiritual leaders and keepers of ancient lore exist in addition to their magical abilities. They only overlapp insofar, that they can consult spirits on complicated questions and they are keepers not only of history and philosophy, but also magical knowledge. They know magic as part of their ancient cultural heiritage. Again, it seems quite appropriate that they are in fact mages who only assume a social role similar to priests, while not actually being weilders of divine power.