Battery

in the case of a battert 'C' typically means something like The 1 hour discharge current.

ie: if it's a 1500mAh battery then C is 1500mA

Historically, the ampere was defined rather recently. The original measurement units WERE charge meters; a Faraday is a defined quantity of charge, that will electroplate a mass of silver in some well defined chemical apparatus.

The ampere unit relates more directly to magnetic force, so for a quick-reacting meter (no need to disassemble the electrochemical apparatus and weigh the cathode) it has come to be the normal measurement.

There is DEFINITELY something wrong with treating storage batteries as capacitors; it ignores the chemical components entirely. Try that with a lead-acid battery, you'll get burned.