Not to worry. It's fine to leave the cable connected. Most of us do that all the time. (Who wants to get up at 3AM to unplug the car when it's fully charged?) The car won't "overcharge" the battery, it's not that dumb.
The "charger" i.e. the circuit that converts AC to DC and controls current flow and battery charging is in the car. It works off 120V - 240V. The huge black brick with the yellow spiral cord is just a fancy extension cable with fancy protection circuitry, called "Level 1 EVSE". For public or home 240V stations "Level 2 EVSE" the protection stuff is build into the wall box or pole, the charger is still in the car.
The "charger" i.e. the circuit that converts AC to DC and controls current flow and battery charging is in the car. It works off 120V - 240V. The huge black brick with the yellow spiral cord is just a fancy extension cable with fancy protection circuitry, called "Level 1 EVSE". For public or home 240V stations "Level 2 EVSE" the protection stuff is build into the wall box or pole, the charger is still in the car.
