There were a few games that worked on the OG gameboy, but were GameBoy color games, the ones that come to mind first are Pokemon Gold and Silver. You could play them on the og gameboy, without color and missing some hardware features, or you could play them on the Gameboy Color as they had intended you do. It was a really nice addition.
I always thought of the GBC as its own generation, since the games were mostly incompatible, just as I thought of the GBA as its own generation for the same reason, but really, it’s almost just arbitrary.