Watts (and Amps if you assume a fixed voltage) are a measure of power. Power is the rate at which energy is being consumed or produced. For a battery, the maximum discharge current * voltage is the power that battery can produce.
Watt hours (and Amp hours assuming a fixed voltage) are a measure of energy. Energy is the ability to do work - in the case of batteries we are specifically referring to chemical potential energy. For a battery the stored Watt hours is the energy the battery has available.
A battery can be capable of producing a lot of power while having relatively little energy (eg the LiPo batteries in an RC car) or can produce a modest amount of power but store a lot of energy (eg a deep cycle battery).