Battery question

That can get REAL involved and confusing, but the answer is irrelevant. Think of it this way. A large water pump fills the municipal water tower, and water leaves the tower to go to your house. Is the water coming from the pump or the tower? The pump is your car's generator. The tower is the battery, and your house is the car's electrical systems.

Another way of looking at it is the generator supplies the car's electrical systems, and some of the extra capacity goes to recharge the battery after running down from cranking the engine. The battery can also supply the electrical systems when the generator is not running.