Capacity is not Capacity
The more electrode active material you have in the cell, the greater is its capacity. Thus a small cell has less capacity than a larger cell, given the same chemistry (e.g. alkaline cells), though they develop the same open-circuit voltage. The capacity of a battery depends on the discharge conditions such as the magnitude of current, the allowable terminal voltage of the battery as well as temperature and other factors.
The available capacity of a battery depends upon the rate at which it is discharged. If a battery is discharged at a relatively high rate, the available capacity will be lower than expected.
The battery capacity that battery manufacturers print on a battery is the product of 20 hours multiplied by the maximum constant current that a new battery can supply for 20 hours at 68 F° (20 C°), down to a predetermined terminal voltage per cell.
A battery rated at 100 A•h will deliver 5 A over a 20 hour period at room temperature. However, if it is instead discharged at 50 A, it will run out of charge before the theoretically-expected 2 hours.
For this reason, a battery capacity rating is always related to an expected discharge duration—the standard duration is 20 hours.
t = \frac Q I
Q is the battery capacity (typically given in mA•h).
I is the current drawn from battery (mA).
t is the amount of time (in hours) that a battery can sustain.
The relationship between current, discharge time, and capacity for a lead acid battery is expressed by Peukert's law. The efficiency of a battery is different at different discharge rates. When discharging at low rate, the battery's energy is delivered more efficiently than at higher discharge rates.
In general, the higher the ampere-hour rating, the longer the battery will last for a certain load. Installing batteries with different A•h ratings will not affect the operation of a device rated for a specific voltage unless the load limits of the battery are exceeded. Theoretically, a battery would operate at its A•h rating, but realistically, high-drain loads, which can occur in digital cameras, can result in lower actual energy, most notably for alkaline batteries. For example, a battery rated at 2000 mA•h may not sustain a current of 1 A for the full two hours.