Is a car's air blower connected to the serpentine belt?

I actually have two question here. The first is whether the air blower (just air no a/c or heat) is connected to the serpentine belt or gets power from the battery / alternator. The second question is about the blower. Sometimes I keep it on off but air is still coming through the blower. Does this happen to you guys as well. Pretty much is the blower always running / getting power from the battery whether you keep it on or off? Thanks a lot for the help guys.