Interesting-- i am sort of the middle of the road-- i use all the terms, and definately see a difference between all of them.
salt box- about the size of a small shoe box, made of wood, with a deeply slanted top.
nowdays, recycled to hold candles or something else.
salt cellar-- a small open dish, with a matching spoon, to serve salt-- my mother's were all fine china or crystal
salt shaker-- a small container, with 1 large hole(UK), or many small holes (US) for table use.
salt grinder-- Like Jo, i too, use sea salt, which comes in larger crystals, that i grind as needed. the grind mechanism is on the bottom, and resessed, so, just placing the grinder down, helps protect the salt.
Salt and pepper shakers--matching sets of shakers for both salt and pepper, some simple, utiliarian, some ornate, and collectors items.. tops usually have S and P patterned holes.
