Our 2008 Chrysler 300c has 2 batteries instead of the usual one. This is common on boats and RVs but not on cars. It has a large battery in the back far away from the starter motor and a smaller battery in the front close to the starter motor. When Barbara left the lights on we went out and jump started the car on the front battery and it started fine. Why don't they separate the batteries for Engine and cabin like in marine applications? Why is the big battery not in the front? What is the purpose of two batteries when it was easy to flatten the system anyway?
The battery is located in the trunk next to the spare. There is a positive battery terminal in the engine compartment located next to the fuse box. Maybe this is what you are referring to as a smaller second battery? It's just a convenient place to access the positive battery connection from the engine compartment.
the 1 at the engine is for starting. the other (called deep cycle), is for supporting all the electronic components that draw a lot of current even if the engine is not running, and otherwise drains the starter battery faster. the starter has more thinner plates, and is more effective for it purpose. the other has less, thicker, and does better for keeping the components alive. the starter is designed for high power short bursts, but hurts if drops below 80%, while the other is designed of longer runs at lower demand, and survives even if going down to 50% systematically. that is why they designed them so. is used in go-karts, for instance. this is a more advanced concept that uses specialized batteries for special purposes, and if properly used-and charged-provides a more reliable system that not only is less prone to getting a battery discharged, but also longer battery life. you can find this in cars like the mercedes SL500.
and there is more: These days some cars will have an extra battery if they're running stupidly powerful stereos, winches or other high power devices without draining the starter battery. These will generally be “deep cycle” batteries, capable of surviving more drain and lower voltages than a typical starter battery.
Mercedes (I don't know about any others) have started fitting dual batteries to power all the standard tech in their top models because there's simply too much drain for just the starter battery.