This is two different things: thermal mass and conductivity.
The moisture you give your fingers to put out the candle provides them with enough thermal mass to absorb the energy from the candle, without dramatically changing the temperature of the water (the water can absorb a lot of energy without changing temperature) Also the water is a better conductor than your skin, so it spreads the energy across the liquid much better.
When you wet an oven mitt, you turn what should be insulating you from the heat into a better conductor, and the heat travels through the water in the glove to burn your hand.
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