Mist= a thin layer of condensed vapor; tiny drops of water in the atmosphere at or near the surface of the Earth: ‘As the day wore on, the early morning mist quickly disappeared.’ ‘The hills were veiled in a fine mist.’
Fog= droplets of condensed water vapor suspended in the air near the ground; very thick mist: ‘Traffic was slowed to a walking pace due to heavy fog.’ ‘Heavy fog made it difficult to see the road.’