In the old days it was more simple. Black was emery, brown was tripoli, gray was medium alumina, white was fine (800 grit), green was chrome, and red was rouge ( very fine).
White diamond was a name brand final high polish. It was not quite as fine as red rouge, but wouldn't stain everything. Everyone pretty much replaced red rouge with it and started calling it white rouge. The FTA got on manufacturers for calling it rouge (red iron oxide), when it was actually a mix of tin oxide and aluminum oxide, so some manufacturers added a tiny amount of red rouge to it and called it things like Pink Rouge and No-Scratch Pink. The Feds eventually gave up on defending the term rouge, and now any fine polish can be called rouge.
Today, there is no guess as what grade it is by mere color. Black can be several grades of coarse. Grey can be almost anything. And, white is a symbol of fineness in a polish as much as a white wedding dress is a symbol of virginity nowadays.
Today, the exact same term can be applied to several polishes ... all of which are different. "White Polish" can range from 500 to 8000 grit.
There is a true rainbow of colored specialty polish compounds including red, orange, yellow, green, blue, and violet. Some of these cost $30 an ounce, others $5 a pound.