The coolant system is not a standalone part of the car instead it has coolant that runs through the entire engine and back through the radiator. The coolant keeps flowing through the system in order to move heat out of the engine and disperse it through the radiator.
The main section of the radiator is used to cool the coolant and the transmission fluid on most cars. The fluids flow across the unit and air passes the fins removing the heat. The cap that is on the radiator is more than your average top to a soda bottle. It consists of a pressure relief valve and spring that will allow for overflow from the radiator to be transferred to the overflow tank.