As far as my experience goes, on an AC charge, if you plug in with the car on, the car will switch to accessory mode (with screen, radio etc. powered). It's then impossible to switch back to 'Ready' mode if you try to start the car.
If you want to stop the charge and unplug, lock the car with the remote, this should power the car off, then unlock with the remote, this will pause charging and unlock the charge port and you can unplug the cable from the car, once the charger sees no load, it should release the cable lock and allow you to unplug from the charger.
Did you drive to the other charger with the cable stuck in the car? This would nean that the charger saw the charge had stopped and released the cable so a problem with the car or possibly the cable.
Can you hear the locking motor in the chargeport operating when you start and stop the charger or lock and unlock the car?