The former is basically just a screen your phone is casting to. The latter is a lightweight (stripped down) Android fork designed to boot very quickly and do a couple things very well. It probably never really “turns off” since it still has a 12v connection even when the car is off (why your clock doesn’t reset).
Android on your phone is a much more general purpose operating system that runs on a (much more limited) battery. It isn’t designed to be turned on and off frequently.