All batteries have some internal resistance so that the voltage will drop as current increases in a reversible way - this limits the useful current from the battery, and can cause excessive heating in large battery packs. As well as the voltage depending somewhat on state of charge this internal resistance will change with state of charge and temperature (each battery chemistry has its own peculiarities).
The capacity will depend on the discharge rate - high discharge rates can reduce the apparent capacity markedly - though what counts as a high discharge rate depends on the chemistry. Because of this battery capacities are usually quoted at a specific rate (often the "10 hour rate"). Capacity of rechargeables will decrease with age and use too.
All of this imperfection and variability means that if you require 2Ah capacity you'd better go and get a 3 or 4Ah battery, and check what discharge rate it can cope with.