Well if you noticed, Oro and Itachi's rings are red, while Kisume is yellow. Speculation here: perhaps it deals with a ranking system within the organization. Red being higher than Yellow...

Or another way could be by category:
Division X: North, East, South, West...NE, SE, SW, NW (?)
Division Y: Scarlet, Blue, Yellow, Green, White...
Division Z: Sky, Fire, Earth...

Or maybe...it doesn't mean a damn thing