The main difference is capacitance; super-capacitors have much higher capacitance than conventional capacitors. As a result,, super-capacitors can store much higher energy because Capacitor_Energy = 0.5(capacitance)(Voltage)(Voltage).

It is also worth nothing that in Power Generation, Transmission and Distribution, there are also capacitors with operating voltages in the range of thousands Volts. Those capacitors store much higher energy levels but they are specialized for high voltage applications. Super-capacitor operating voltages are limited to few hundreds volts.

You can see some more information at:

https://www.researchgate.net/publication/254708421_Discrete_linear_constrained_multivariate_optimization_for_power_sources_of_mobile_systems

Thesis Discrete linear constrained multivariate optimization for po...

Conventional capacitors use solid dielectric medium between the electrodes. To the contrary, supercapacitors use liquid electrolytes to separate the two electrodes. Typically, supercapacitors have much higher capacitance than the conventional capacitors. Both are used for energy storage but the supercapacitors are capable of storing more electric charge. With respect to cost, supercapacitors are more costly than the conventional ones.

Hope this helps answer your question.

Professor Yehia Khalil

Yale University

USA