There is absolutely no difference between fog and clouds found high in the air. Fog is simply a cloud that has formed near the surface of the Earth. There are four main types of fog: Radiation fog, advection fog, upslope fog and evaporation fog.
Radiation Fog
As the ground becomes cooled by the night sky, the air above the ground also gets cooled. This can bring the air down below its dew point, causing water vapor to condense around the dust and other particulates in the atmosphere creating fog.
Advection Fog
Similarly, advection fog takes place when warm air moves in horizontally over a cool surface, such as when air from the ocean blows in over land. The land cools the air down below the dew point, causing fog to occur.
Upslope fog
Upslope fog takes place as warm air passes over the slope of a cool mountain as it rises. The mountain cools the air below the dew point causing it to condense, forming fog.
Evaporation fog
This final form of fog is caused when additional water vapor enters air that is already near the maximum vapor pressure. Because the air is already nearly saturated, the additional water vapor causes the air to reach the dew point, forming fog.