The Super GameBoy would only run cartridges that are compatible with the original monochrome GameBoy, although there is a capability to map the 4 shades of grey to various colors on the TV. Some later GameBoy games had additional color information or display frames provided for use by the SGB.
The link port needed to connect two GameBoys together was not present on the SGB, although it was added to the Super GameBoy 2, which was only sold in Japan.
No version of the Super GameBoy is capable of running games that are designed for the "GameBoy Color", although they will run dual mode cartidges in GameBoy mode. The only official way to run Color GameBoy cartridges on a TV set is using the GameBoy Player on the Nintendo GameCube.