TLDR : Are the plates of a battery more like a capacitor with excess charges on the plates?
Yes. This is why a (charged) cell has a non-zero open-circuit (no external circuit) voltage across. Despite the fact that there is no external circuit through which charge can flow, the reactions of the plates with the electrolyte result in one plate having a deficit of electrons (positively charged) and the other plate having an excess of electrons (negatively charged).
Essentially, it is this separation of charge (and the associated electric field) that 'halts' the (net) chemical reactions at the plates and produces the constant open-circuit voltage.
If electrons are allowed to flow through an external circuit (load) from the negative plate to the positive plate, the reactions proceed and the cell discharges.
In the case of a rechargeable cell, an external source can move electrons from the positive plate to the negative plate essentially reversing the chemical reactions at the plates and the cell charges.
(From the comments)
OK but when we connect both terminals with a circuit wouldn't all the excess charge simply flow in the wire and terminals become neutral again ?
Unlike a capacitor, the energy stored in a cell is in the form of chemical energy and not electrostatic energy. Only a tiny fraction of the stored chemical energy is needed to establish the open-circuit voltage.
Like a capacitor, the plates have equal and opposite electric charge but unlike a capacitor, chemical reactions 'try to' maintain the charge separation on the plates even as excess electrons flow from the negative plate, through the load, an onto the positive plate.
Of course, there is a limit and cells have a so-called short-circuit current that is the maximum current that can be supplied when the plates are connected together with a wire (I should point out that this is generally not a safe test to perform).
There is of course, lots more to all of this, and I do believe there's some good Q & A here on this subject.