The GameBoy Color is indeed the successor to the GameBoy and a separate system, but at the time, Nintendo didn't see a reason to bother with drawing a difference in the books. They still sold various versions of original GameBoys, and many games were still made compatible with original GameBoys.
As for the game compatibility, Nintendo designed the GBC's hardware similarly enough to the GameBoy's that many games could be created to be compatible with either. Plug it into a GBC, it reads that it's in a GBC and sends out a color signal. Plug it into a classic GB and it sends out the classic four-color black-and-white. It's... pretty simple.