Granite grit is harder than many other types of rock and will last longer. However, chickens themselves don't know the difference between dolomite, granite, quartz or any other type of rock. If they are free ranging, they will use whatever is available. If it happens to be a softer stone like limestone, it will be ground up faster than a granite and will pass through their system. They will then have to eat more to replenish the grit in their gizzard so they can grind up their food. As long as the stone is harder than the bug shells or grains they eat, it can be used as grit.
Granite is the standard that you buy because it is harder and lasts longer. I'm not sure where the granite grit we buy comes from. I'd guess it is a by-product of some process that makes it cheap and readily available.