Step back and take a deep breath, boys... you're both right in places.
Capacitors store energy in the form of electrical charge, but batteries store energy in chemical reactions. Putting a load across a capacitor causes a flow of electrons (current). The chemical reaction during battery discharge liberates electrons (also collected as current flow).
Keep in mind that some of the previous argument ignored that there are two kinds of batteries. A
primary battery is used once and discarded (carbon-zinc which has been mostly replaced by alkaline, for example). A
secondary battery is the kind we put in our Mopars, and is recharged with electrical energy that is stored as chemical energy...
A lead-acid battery is indeed charged when the electrolyte is added, because the chemicals have been placed in the high-energy state at the factory! Used to be called "dry-charged". The positive plate is lead oxide, and the negative plate is lead. As it discharges, the plates
bothturn into lead sulfate, and electrical charge is liberated from the negative plate. That's why the electrolyte is sulfuric acid - you need that sulfate ion.
See, for example,
https://www.pveducation.org/pvcdrom/batteries/lead-acid-batteries for more than you probably wanted to know
Once the lead-acid battery has been discharged, you
cannot get more energy out of it except by forcing current into it and reversing the chemical reactions (back to lead and lead oxide). Yes, it will recover a bit if it hasn't been 100% totally killed flat dead. Let it sit discharged long enough and the lead sulfate crystals grow to a point where they can't be easily removed, if at all. Then you recycle it.
There is even more to it, of course, but that should be plenty for now
Hope that helped.
-Charles
(EE since 1981).
