Two modes of electrostatic force with charged capacitors?
Parallel plate capacitors with no material between the plates use the electric and magnetic field to store energy.

It depends on what the material is between the plates. The simple parallel plate is assuming no dielectric. The electrolyte is a dielectric material which has a high charge density than that of air (or vacuum). This enables one to store more charge in a material with a dielectric than that of air in a simple parallel plate capacitor.

Supercapacitors work on a different principle to increase the amount of charge.


  In a supercapacitor, there is no dielectric as such. Instead, both
  plates are soaked in an electrolyte and separated by a very thin
  insulator (which might be made of carbon, paper, or plastic). When the
  plates are charged up, an opposite charge forms on either side of the
  separator, creating what's called an electric double-layer, maybe just
  one molecule thick (compared to a dielectric that might range in
  thickness from a few microns to a millimeter or more in a conventional
  capacitor). This is why supercapacitors are often referred to as
  double-layer capacitors, also called electric double-layer capacitors
  or EDLCs). If you look at the lower diagram in the artwork, you'll see
  how a supercapacitor resembles two ordinary capacitors side by side.


Source: https://www.explainthatstuff.com/how-supercapacitors-work.html