They use a different machine to make stone marbles. They are called sphere machines. The older, valuable stone marbles were actually ground by hand and display very tiny facets over the surface.
The video gives you a good idea of how machine made marbles are made. The hot glass is pinched off and drops into the corkscrew, where it is formed into its round shape. Multi colored marbles are a bit more difficult to produce because you have to feed the different colors of hot glass together at the right temperature and speed in order to get the right look. The cullet is actually a malfunction that occurs when the hot glass marbles stop advancing along the screws and bunch up. They have to be cleared out by the operator. As would sometimes happen, the glass might over-mix and the colors would "blend" together too much. That is where the term "blended" comes from when you see one for sale online. A blended marble is actually an error marble that is only found in the dumpsites. These error marbles are usually more valuable than the proper production marbles because much less of them exist. Most of the blended errors are much prettier and desireable than their proper counterparts. I will be posting some blended marbles soon for you to see.
I don't know a whole lot about cateyes so I won't comment on them until I find out more about the process.