... Would someone please explain how storing and releasing electricity in a cap can change tone. ...
It couldn't,
if caps behaved as an ideal capacitor.
In real life, they don't behave as an ideal capacitor, due to tradeoffs in materials used and construction method.
To see an equivalent circuit of a real (aluminum electrolytic) capacitor, look at the top of page 6 of this
Cornell-Dubilier Application Guide. Don't get lost in all the other stuff in the guide.
Different construction techniques and different dielectrics (the insulator) are used to produce a desired capacitance and voltage rating in a desired-size package. General rule of thumb is the more capacitance per square inch (or cubic centimeter), the more parasitic components will move the cap's behavior from that of an ideal cap.
CAVEAT: An air-dielectric cap may have the closest performance to an ideal capacitor (based on the qualities of the dielectric), but its size for a given capacitance may be so big that now cap self-inductance becomes a factor.
BUT... there's a lot of fairy dust and marketing out there. The audible differences between most, say film, caps used for coupling cap duty are generally pretty small in my opinion compared to a change of cap value. The point of diminishing returns is quickly reached.
Bottom line is that there are generally good general choices you can make for a cap for a particular application; tweaking beyond the general choice is unlikely to return significant benefit.