Yes, there are different types. The most common types are Battery Electric Vehicles (BEVs), Plug-in Hybrid Electric Vehicles (PHEVs), and Hybrid Electric Vehicles (HEVs).
BEVs are often referred to as All Electric Vehicles as they do not have an internal combustion engine.
PHEVs utilize both an electric motor and an internal combustion engine and will often run on electricity until the battery has been drained, and then switches to its gasoline engine. PHEVs can be plugged in to charge the battery.
HEVs also have both an electric motor and internal combustion engine. However, they cannot be plugged in to charge the battery. The electric motor element of the vehicle allows the car to get significantly higher fuel mileage.