We do tend to use imprecise terms for the physical quantities. It sometimes isn't a problem. But of course we should switch to precise terms when needed, typically in a logical chain of argument but often in a disagreement.
Battery capacity is measured by the energy stored, not the power. It isn't possible to measure power in watt hours.
It's also better to leave units of measure out of it until the type of quantity being discussed is clear. Energy and power are different types of quantity whatever units are used.
Jonathan