Most, if not all, "hybrid" vehicles will have a high voltage bank of lithium batteries for propulsion in addition to a 12v lead acid battery to run the chassis electronics.

I am aware of three basic patterns of hybrid cars, which I will call:

-Electric Vehicle That Lugs A Generator Around With It. Example: Chevrolet Volt. The car is propelled with electric motors only, and it is intended to operate primarily from battery power recharged from the power grid. For range extension, it has a small ICE engine that turns a generator, which will only start and generate power when the batteries are low. There is no mechanical transmission; the engine cannot directly drive the wheels.

-Why Not Both? Example: Toyota Prius (Early models at least; I think they make a full EV badged as the Prius now). The car has an internal combustion engine, a mechanical transmission, batteries and motors. They're exact modes of operation vary from model to model, but generally these will stop the engine and operate on batteries when stopped, coasting, braking, operating at low speed, or sometimes cruising. They will start the engine and run on engine power while accelerating to highway speed, possibly cruising at highway speed, to run accessories like air conditioning, or when the batteries are low. These may or may not plug into the power grid to recharge their batteries, or they may ultimately derive all energy from gasoline. Again the exact implementation varies from model to model.

-Two Ton Golf Cart. Example: Chevrolet Silverado. You'll see these marketed as "soft hybrids," "mild hybrids" or "stop-start". Sometimes these just have extra big normal batteries, sometimes these have relatively small lithium batteries. These are more or less normal cars that are anal retentive about how they burn gasoline, shutting down the engine when coasting, braking, idling or sometimes moving at very low speed. Depending on the implementation, the car might just have an extra big starter motor that starts the engine in gear when you push the gas pedal, so the first 3 feet or so are done under battery power and then you're under gas power. Some can decouple the motor and engine and kinda have "electric first gear." Maybe you can make it through the McDonald's drive-thru purely on battery, but it'll start the engine if you hit 10MPH or so. You often see this in larger, heavier vehicles like pickup trucks where the additional electric powertrain would be very heavy and very expensive, but just shutting down the engine sometimes can gain some MPG.