Lots of good points and we do not need to sweat the details. Typically single phase motor start capacitors are electrolytic non-polar because of the uF size and voltage, other types would be too large. Also because the start winding is only 1/2 the phase you sometimes see the capacitor voltage rating of 125VAC and not 250VAC. But I also have single phase motors that use a single start/run capacitor that is a non-electrolytic (typically a non-polar oil type). Non-polar electrolytic are designed typically to pass AC voltage/signals and the construction as I understand it is two serial back to back electrolytic capacitors in the same housing, although I do not know the exact construction. They do not have internal diodes, but the construction is such that it is modeled with two diodes. The takeaway message is that in an AC system the capacitors/ratings are very different between AC and DC voltages, so that in an AC system one needs to specifically use a capacitor for the AC voltage rating. When a single phase motor often does not start and just hums, (excluding a short) the start capacitor typically fails, in particular with repeated start/stops because of the thermal heating. One reason why I recommend 3 phase motors in mills and lathes being turned on/off frequently. Run capacitors are usually oil filled or may be solid non-electrolytic types. The quality of the capacitor plays an important part of its longevity, also how long it has been sitting around on the shelf. Old electrolytic are exactly that, old and prone to failure. On VFDs sitting on the shelf, they recommend powering them up at least once a year under no load to reform the electrolytic capacitors.
