The other terminal is connected to the glass bulb, which does not readily conduct electricity. Everything may not be okay, if the alternator was failing to charge the battery. But in most cases, the alternator will provide sufficient charge to the battery after a few minutes for it to be able to start the car. Heat energy is the graveyard of all forms of energy. It depends on the appliance.
Damage generally occurs by excess heating caused by too much current driven through the wires.
This can happen a couple of different ways. For an appliance that converts electrical energy directly to heat, this happens when excess voltage is applied. For an appliance that uses an electric motor, too little voltage can result in overheating that burns up the motor windings. To be safe, use the recommended voltages with appliances of any kind. Fortunately car headlights are wired in parallel so that when one goes out the other will still provide some light.