Well, it's a bit more complicated that that:
-Red, Green, Blue, and the Japanese version of Yellow were "grey cartridge" gameboy games, which means they were designed with the monochrome gameboy in mind. The entire game can only for 4 distinct colors for the entire game when played in a GBC, a default pallet and and a bunch of optional ones from pressing button combos on the gameboy boot screeen. Of these titles, all but some of of Gen I Pokemon games defaulted to the Green/Blue/White/Black color pallet when played in a GBC. Some games had enchanced color pallets when played on the SNES Super Gameboy, but most default to an orange/brown/white/black pallet but it could be customized in the settings.
-The Interational version of Yellow, and all versions of Gold and Silver, have "black cartridge" games, games that have full color when played in a GBC(and thus say GBC on their boxart), but are compatible with with the original game boy. In yellows case, it was less of full color and more that they simply made it use the enhanced colors used when played on the Super Gameboy awhen played in a Game Boy color system. Black cart games played in a Super Gameboy(outside of Yellow) default to the orange/brown/white/black color pallet like most grey cart games but unlike them it cannot be customized.
-Crystal was a "clear cartridge" game, a game that only works on the Gameboy Color and does not work on the original game boy. These used more advanced color palettes than the Black Cartridge games and usually used the GBC's better processing power, neither of which could never be utilized in Black cart games. These games cannot be used on the Super Gameboy at all, giving the same error message they do if you put them in a Gameboy Pocket or Gameboy Light(the original fat model can only turn on with clear cart games in them if you broke off the little nub in the cart slot)
Also fun fact, in Japan Crystal was the only game among these to have a colored cartridge(it was actually more elaborate than ours, because Suicune's head crest was etched into the board inside the cart). The Gen 1 games used the original grey carts and Gold/Silver used the black carts.
