Each of these components is very basic in its function and its relationship to each other. A battery is an electrical reservoir. You put electricity into it, and you can take electricity out of it. When you puts lots in, the battery reaches a full charge and when it's full, it's full. You can't have more than a full charge.
Batteries can store different amounts or volumes of electricity, expressed in amperage.
When you purchase a battery for your car, you will be asked how big a battery you want. What the salesperson is asking is what amp capacity you want -not the physical size. The more amps, the better. You are buying insurance, so to speak, when you purchase a big battery. It will get your car started on a cold winter's day or if you accidentally leave your lights on and go shopping for two hours.