Yeah, you've probably got a GameBoy Color link cable.
It can physically fit inside the GBA's port, and you can use it to connect a GBC game (like Pokemon Gold/Silver/Crystal) to another GBC game, even if one or both of the GBC games are running in a GBA.
Basically, think of it this way. When you have a GBC game in your GameBoy Advance, it stops being a GameBoy Advance, and transforms itself into a GameBoy Color.
You need a GameBoy Advance-specific link cable. It has like... higher bandwidth... or something. And connecting GBA games won't work without it.