What is the difference between mist and fog?
Quoting from the METAR decoder:

BR Mist (Foggy conditions with visibilities greater than 5/8 statute mile) 

FG Fog (visibility 5/8 statute mile or less)


You may ask "Why 5/8th of a statute mile?"  That's because 5/8ths of a mile is 1,006 meters, or about 1 kilometer.