The Priest class in World of Warcraft.
Doesn't have much more to do with Cleric than it does with Psionicist, so that's a bizarre comparison.
Whereas the Paladin class in World of Warcraft is pretty much a D&D Cleric if they're Holy spec'd. WoW Priests though? No. Absolutely not. They're a completely bizarre and wild class that just doesn't exist in D&D (the closest maybe being 4E's Invokers?), which a Light/Shadow motif and also have some psychic powers stuff.
White Mage in Final Fantasy.
It doesn't just lack the robes, it also lacks the "Holy Warrior" aspect. Instead it's thematically rather closer to Druid in most of Final Fantasy where it appears. They're focused on nature and life and healing.
Almost any organized religious figure in most fantasy stories.
An extreme claim that requires extreme evidence.
Of which there is, as keen reader of fantasy literature, I assure you, little to none. It is simply not an accurate claim.
Most religious figures in most fantasy stories have no supernatural powers whatsoever, or where they do, they tend to be somewhat creepy ritualized powers that lean towards what D&D calls Arcane magic, or beseeching supernatural entities.
The only real difference is that these fantasy priests are wearing priestly smocks, nun habits, or monk robes in place of armor.
No.
As I've illustrated and can happily illustrate in considerably more depth, this simply is not true. The vast majority of "fantasy priests" simply do not have powers. Even when they do have powers, they're often arcane powers, from learning, rather than the divine.
The only figures I can immediately think of in fantasy who even vaguely resemble D&D Clerics tend to get called things like "Paladin" or "Warrior-Priest". For example, in Warhammer Fantasy, which derives heavily from D&D, the Warrior-Priests of Sigmar have abilities which line up relatively well with low-to-mid-level D&D Clerics. Because they're inspired by D&D Clerics. They're even armoured and tend to use hammers (albeit to honour Sigmar rather than any other reason). They in turn inspired WoW's Paladins, who are also quite Cleric-like, especially if spec'd Holy.