What does it mean when the left side of your radiator was smoking and it damaged the radiator cap when you took it off there was a lot of coolant in the radiator?

Your water pump might be broken or your thermostat might need to be replaced. You obviously don't have a leak so somehow the fluid isn't moving through the engine. If the thermostat is broken it will not let fluid into the engine and then the engine will overheat and the radiator will release smoke.