The car still has a combustion engine which burns fuel and powers the AC power generator, or alternator. The typical automotive 12V lead acid battery is a rugged secondary (rechargeable) battery and is coupled with an alternator. The standard lead acid battery is necessary, as a regular part of a combustion and electric powered car, because why reinvent the wheel, as is said.
Even though a hybrid car has battery power stored within its chassis, that battery power is solely meant to provide electrical power to the total power, adding to the combustion-derived power.
A hybrid has an engine like a typical car and so it needs a secondary battery which recharges well, with low internal resistance, but which also provides power for the stereo, the lights, etc.
The lead acid engine battery is a separate entity from the lithium battery [banks] of the electrical portion of the hybrid.
Lithium based batteries, often lithium polymer or LiPo, also have low internal resistance.
Lithium batteries typically have reasonably good lifetimes in terms of total charge-recharge cycles over time, similar to car batteries. (Better than other, older secondary batteries such as the nickel metal hydride NiMH which developed “memories” and had shorter “lifetimes” based on total charge/recharge cycles)
Directly shorting the terminals of lithium batteries (connecting postive to negative) is potentially very dangerous as this creates a very strong current flow as a short [circuit]. This is similar to car batteries, when accidentally shorting the poles (+ / -) with a metal conductor, e.g. a wrench, there is a large current discharge.
The batteries have different roles in the car's function.
