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> It is the correct tern, physically.

Agreed, but not from a consumer perspective, where it is very confusing that a battery with half the capacity might have twice the energy due to differences in voltage.

From a consumer perspective, the battery capacity is the amount of energy, regardless of whether that is wrong.

I don't think "capacity" neccesarily has a concrete unit connected to it. I am pretty sure you could call both the charge and the energy in a battery its capacity.

> Not the natural unit though, that would be Coulomb (C).

To be pedantic, you mean SI unit. The natural unit of charge is the electron (e).