Arkansas stones are just that, a natural stone.
Several grades of hardness.
India stones are synthetic and a trade name of Norton Abrasives as geddylee points out.
These are man-made Aluminum oxide abrasive stones in differnt grades of grit.
Different colors ID the different grit.
Other abrasive makers use aluminum oxide to make polishing stones as well, they just can't use Nortons 'India' trademarked name for them.
Crystolone (sp?) is the fastest cutting of the bunch and also of man-made but these are of silicon carbide grit. Crystolone is again a tradename of Norton Abrasives and other mfg's make the same thing under different marketing names.
These silicon carbide stones cut fast , very aggressive and work well as a first step in 'stoning' a surface flat.
All of the above are 'oil stones' .
The water stones are aluminum oxide grit AFAIK in several grades and wear quicker than the India aluminum oxide (oil) stones because of the matr'l that is used to hold the grit together to form the stone breaks down easier.
Sometimes called Japanese Water Stone.
These cut fast but the soft nature of the stone breaking down can leave it with less than flat surfaces. Sometimes that tendency to conform to a rounded surface is used to an advantage however.
Use plain water for the lube makes them nice to work with.