Fog is formed when moist air near the surface is cooled sufficiently for its water vapour to condense into water droplets. The process is indentical to that which creates clouds.
Hill fog is formed when moist air moves inland and rises over high ground, cooling and condensing as it goes.
Radiation fog is formed over land on clear, quiet nights, when the land cools quickly, radiating its heat into space. This, in turn, cools the air in contact with the land, allowing its water vapour to condense into fog, which may drift out to sea. It is common in coastal waters in winter and spring, especially near large towns, but generally clears during the morning and seldom extends more than a few miles offshore.
Advection fog or sea fog is formed when warm moist air flows over a colder sea surface which cools the lower layers of the air. It is particularly associated with cold ocean currents, but around the UK it is common in winter and spring, when the sea is at its coldest. Sea fog may last for days on end, and is not ´blown away´ by the wind: on the contrary, a SW wind may feed the fog by providing a continuous supply of moist air.
Frontal fog may form along a warm front or occlusion, especially if the air ahead of the front is very cold. It is caused by the warm air mixing with or being cooled by the colder air ahead of it, so it is very limited in extent, but may give way to sea fog in the warm sector.
Arctic sea smoke, despite its name, is not confined to the Arctic! It is formed when cold air flows over a relatively warm sea. As it does so, the air in contact with the sea is warmed up and absorbs moisture. As it warms, it rises, and is immediately cooled by the cold air above. The process is very similar to that which goes on above a mug of hot tea! Around Holland and the UK it is rare at sea, but is quite common over rivers and estuaries on frosty winter mornings.