An alternator can be spun much faster than a generator because of its internal construction. With a small diameter pulley, that means the alternator can produce enough current to keep the battery charged at idle. A generator must be revved up above idle to produce enough current to keep up with the demand of things like headlights, heater blower, electric wipers, and other drains such as stupid-high wattage sound systems, etc. The alternator can handle all those loads, and still have some amperage left over to charge the battery.
Jerry