Marketing :) US, casual, non-scientific usage: Pigeons are gray and live in cities. Doves are white. Mist is when the air is full of fine droplets of water. It is not heavy enough to actually be rain, but if you walk around in mist, you will get wet. It does not obscure your vision. It's just wet. Fog *does* obscure your vision - you can't see through it. It is drier than mist.

The family of birds called Columbidae contains several species that are called pigeons or doves but there isn't a clear definition of what differentiates the two. Doves are generally smaller, have longer tails and are not usually domesticated. Pigeons are the birds that live in large flocks in urban areas. But there are some kinds of pigeon that are also called 'rock doves'. Mist and fog are the same thing, but mist lies close to the ground and you can see over it. Fog means a lot of mist that extends from the ground up high enough to obscure one's vision.