Alex is correct. Caucasian doesn't refer to just "white" people. There are many Indians with "black" or light to medium dark brown skin. I think that somewhere over the years Caucasian became synonymous with white skin. Usually, at least in America, white on an ID form refers to someone who would be socially white. Many Indians will put down Asian, although in America Asian tends to refer to central Asians.
Outside of white and black America, most people use a combination of hair texture, facial features, body type and skin color to describe racial characteristics, instead of just skin color.