As jason says, SG and Spheroidal Graphite Iron are one in the same and are usually specified for high stress applications such as Model traction Engine crankshafts. This is also called ductile iron and exhibits many of the structural properties of some steels whilst being easier to machine.
Grey Iron is best suited to engine cylinder heads and blocks, gears and machine slideways but does not have the ductile strength of SG Iron.
White Iron is unalloyed cast iron with low carbon and silicon content such that the structure is hard brittle iron carbide with no free graphite.Very limited in its applicable use as it has a low impact resistance.
There are many other grades of cast iron that exhibit differing properties and it really depends on the application as to what type you require. This is also applicable to steel as this also comes in varying grades such as EN1A EN8 EN24 etc etc all with differing properties. Then there is stainless, bronze et al.
Maybe DC can put in an article or two covering the different grades of these materials and their application, if this has not been covered already.