Failed electrical engineering major here - it turned out I was built to be a scientist, not an engineer, but it took a year of EE classes to figure that out.

Regarding energy storage, capacitors aren’t much different than batteries, but they can charge/discharge faster, have lower energy density (units of stored energy per units mass), and self-discharge faster, hence why they aren’t used in place of batteries. For something where weight and volume aren’t an issue and with no need for long-term storage, like a solar-equipped house, a huge cap would be a great option. I’m trying to figure out how to build one of what’s described it the article now.

The rate at which a capacitor discharges varies just like a battery, proportional to the resistance of the circuit. The reason most folks associate capacitors with “shorted terminals go boom” is the maximum rate of discharge on a capacitor is much higher than a battery, plus some capacitors operate at a much higher voltage than is practical for a battery, increasing the likelihood of generating a small arc. Shorting the terminals with a conductor makes a low resistance circuit so it just dumps its charge, whereas a battery would max out at a much lower rate, typically making a toasty wire versus a vaporized or melted wire.