= Solution
An ordinary <capacitor> stores <energy> by separating charge across a <dielectric>: $E=CV^2/2$ and $Q=CV$. Electronic charge redistribution is rapid, giving high <specific power>, but the <dielectric> breakdown field and modest <capacitance> limit <specific energy>. Series resistance limits pulse power and produces heating; a large nominal <capacitance> does not remove those losses.
A <supercapacitor> has a much larger interfacial area and nanometre-scale charge separation. An <electric double-layer capacitor> stores charge without a bulk <redox> transformation; <pseudocapacitance> adds sufficiently fast surface or near-surface <redox> storage. <ion> motion in pores, <electrolyte> stability and series resistance constrain its response. Its <specific energy> usually exceeds an ordinary <capacitor>'s while high <specific power> and cycling durability remain possible.
An <electric battery> stores chemical <free energy> through coupled <electrode> <oxidation-reduction reactions>. It can store substantial <energy> per <mass>, but charge transfer, ionic transport, <diffusion> and heat removal constrain rapid discharge. The terminal voltage and accessible capacity depend on discharge rate and state of charge. Accordingly the plotted order follows the storage and transport mechanisms; it is not a claim that every <battery> has less power than every <supercapacitor>.
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