The ambient air temperature that we see reported in our METARS is also referred to as the 'dry bulb' temperature. It is measured in the shade of an instrument shelter, normally about 1.2 metres above ground level. Traditionally, it was measured using a mercury thermometer, but it is now measured electronically using a resistance temperature device.
The dewpoint temperature cannot be measured directly, it must be calculated. Traditionally, this was done by recording both the 'wet bulb' temperature and the 'dry bulb' temperature. The 'wet bulb' temperature was measured by an identical mercury thermometer right beside the dry bulb thermometer in the same instrument shelter, only it had a wet cotton muslin wrapped around the mercury bulb, with a wick attached to a reservoir of distilled water to keep the muslin moist. Because the muslin is moist, whenever the relative humidity of the ambient air is below 100% evaporation is occurring and we all know that evaporation absorbs latent heat, so the wet bulb temperature will always be lower than the dry bulb (except when humidity is 100%). The lower the humidity, the greater the difference between the the dry bulb and wet bulb temperatures. By calculating the difference between the two temperatures and looking up a table comparing this difference to the current dry bulb temperature, the dew point temperature could be found (a separate chart used the same figures to calculate the relative humidity). At Bureau staffed meteorological stations this process continues today as it is the most accurate method for determining the dew point (and relative humidity). These days the wet bulb temperature is also measured by an electronic resistance temperature device with a combined wet muslin/wick fed from a distilled water reservoir. The calculations are now done using algorithms by computer rather than referring to tables. You are are unlikely to ever come across the wet bulb temperature because it isn't published anywhere, it is simply used to calculate the dew point and relative humidity.
When the relative humidity is 100% (which by the way does not occur only in fog - it is common during heavy precipitation and blizzards as well), the dry bulb, wet bulb and dew point temperatures are all equal. When the relative humidity is less than 100%, the dry bulb is always greater than the wet bulb temperature and the wet bulb temperature is always greater than the dew point. For example, I live in the tropics and right now the dry bulb temperature is 28.8C, the wet bulb temperature is 26.7C, the dew point temperature is 25.9C, and the relative humidity is 85% (yes it's build-up time!). Because the humidity is high, these temperatures are quite close together - but in dryer conditions the temperatures are very different.
So, the wet bulb and dew point temperature are not the same thing and if you ever happen to get hold of a wet bulb temperature (probably from a BoM office), please don't substitute it for dew point temperature in your aviation calculations.