The current that can be delivered by a battery is a function of its capacity (Ah), voltage at the terminals and load + internal resistance. Ah is indicative of the amount of energy stored in the battery, which goes down as the internal resistance increases due to discharge, sulfation and grid corrosion. Internal resistance can be reversed with charging but up to a point and depending on factors such as age, no. of charging cycles, condition of cells, etc. As others mentioned already, the open terminal voltage of a battery does not correspond to the battery's capacity. As an example, if you connect 2 identical batteries in parallel, you will double the capacity (Ah) but not the voltage.