As the name suggests, submersible sump pumps sit inside the pit. They use a float switch gauge to determine when the water level is too high and thus when to activate the sump pump.
Pedestal sump pumps sit above the pit to ensure that the motor does not touch the water and thus malfunction. They work similarly to submersible sump pumps.
Battery-powered pumps are primarily used as backup/emergency systems. The benefit of having a battery-powered pump along with your regular system is in case you lose power. Your emergency sump pump can easily kick in and continue pumping out water to prevent a flood during a power outage, which often accompanies heavy rainfall.