From Old English 'mist,' from PIE *h3meygh- — predating 'fog' in English by about 800 years.
A cloud of tiny water droplets suspended in the atmosphere at or near the earth's surface, limiting visibility to a lesser degree than fog.
From Old English 'mist' (mist, fog, dimness, obscurity), from Proto-Germanic *mihstaz (mist, fine vapor, fog), from PIE *h₃meyǵh- (to drizzle, to urinate, to make fine moisture). The PIE root *h₃meyǵh- is a remarkable convergence of the mundane and the meteorological: it referred to the emission of fine moisture in any context, covering both rainfall as fine droplets and the voiding of urine, with the common thread being diffuse liquid. This root gives Sanskrit 'mehati' (he urinates), Lithuanian 'mìgla' (mist, fog), Russian 'mgla' (mist, haze), Greek
In German, 'Mist' does not mean fog — it means 'dung' or 'manure.' The German word for fog is 'Nebel.' This is a false friend that has tripped up many a language learner. The semantic shift from 'fine spray' to 'excrement' in German likely followed the path: fine moisture → urine → animal waste generally. The English