"thick, obscuring mist," 1540s, a back-formation from foggy (which appeared about the same time) or from a Scandinavian source akin to Danish fog "spray, shower, snowdrift," Old Norse fjuk "drifting snow storm." Compare also Old English fuht, Dutch vocht, German Feucht "damp, moist." Figurative phrase in a fog "at a loss what to do" first recorded c. 1600. Fog-lights is from 1962.
"long grass, second growth of grass after mowing," late 14c., probably of Scandinavian origin; compare Norwegian fogg "long grass in a moist hollow," Icelandic fuki "rotten sea grass." A connection to fog (n.1) via a notion of long grass growing in moist dells of northern Europe is tempting but not proven. Watkins suggests derivation from PIE *pu- (2) "to rot, decay" (see foul (adj.)).