It’s a matter of surface area and water being a great conductor of heat.
A candle is very hot but only a small point at the end of the wick is actually burning. if you snuff it out with wet fingers, that tiny point of heat is distributed across the much greater surface area that is your fingers squished together and you barely feel it.
A pan is large and thus contains *vastly* more actual heat energy. The metal of the oven mitt is a great conductor, as is water in a wet oven mitt. All of the heat from the pan is conducted almost instantly through the water and into your hand. The surface area ratio of “hot thing : hand” is much greater with a pan than it is with a candle, and all the heat from the pan doesn’t “go out” instantly like it does with a candle. It just keeps pumping heat in until the temperature of the pan and your hand are the same.
Even if they were the same temperature to start with, there’s very little hot matter in a candle flame compared to the hot pan. The total amount of energy in a candle flame at any given time is quite low, and the water on your fingers is sufficient to absorb the heat by the time the flame goes out. In contrast, a pan hot out of the oven holds significantly more heat, enough to heat the water in the mitt to sufficient temperature to burn you.
A thin layer of water can *very* briefly protect you from hot temperatures by absorbing the energy and evaporating before the heat transfer reaches your skin. For an object with very little residual heat like a candle wick, this is sufficient.
A much more massive metal pan has vastly more heat to give, and the large volume of water only serves to conduct it to your hands more efficiently.
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