How do they produce batteries with the same voltage but different current?
A 12.6V battery is made from 6 2.1V cells. The voltage of each cell depends on the chemistry of the battery. Two metals and an electrolyte will make a particular voltage. In the case of lead-acid battery, lead and lead dioxide are the metals. The electrolyte is aqueous sulfuric acid. This combination makes 2.1V nominally. 

The current capability of the cell depends on the surface area of the cell. One square inch of surface area will be capable of less current than ten square inches. The surface area will add to the size of the battery. The greater the current capability the larger the battery physically.