The Super Game Boy is a "Game Boy in a cartridge", which reads Game Boy and Dual-mode Game Boy Color cartridges, passes the video and audio out to the SNES system for play on a television, and uses SNES controller.
The Super Game Boy would map the 4 grey shades of the Game Boy game to color palettes selected by the user. Game Boy Color games utilize the Game Boy greyscale coloring, and not the full color spectrum.