Sorry, I don’t know much about cars (hence why I’m here to ask things).
You are correct, it was the refrigerant they took out from the car. They said there was only a little bit left, caused by a leak somewhere in the AC system. They performed some kind of vacuum test on the system to determine that there was, in fact, a leak somewhere. They then refilled the refrigerant along with a dye so that they could identify the leak at a later point.
So, yes, it is the AC system that has a leak, not the engine coolant system.