To go back in history just a bit, the original rhinestones were actually Quartz pebbles from the Rhine River (thus their name). Once those stones were depleted for jewelry the rhinestones we know today were made from glass, some leaded, others not, and they were faceted and normally backed with a “foil”. This “foil” is what brings the color to the present day stones.
Paste stones are antiques with their roots traced back to ancient Egypt. These stones were made with glass that was ground into a paste. The gem was molded and then it was melted. It does not resemble the rhinestone of today for it was opaque with a frosted surface.
That being said, today many people do use the word “paste” and “rhinestone interchangeably.