There are some concept explanations here: Texas Avenger "TA" Driver series - Triple channel + Bistro or Narsil + Clicky or E-switch - The Ultimate open source driver!
If you grasp the concept of that, then here is a more technical description:
With OTSM you have an interrupt monitoring power on a IO pin. As soon as power off is detected, the code needs to shutdown everything and put the MCU in to low power sleep mode, waking it up in small periods (0.125 seconds in may case) to check weather power is restored. Each wake up cycle is counted, and this number is read when power is restored. Then you know exactly how long the flashlight was off (with 0.125 accuracy in may case). OTSM requires a larger cap because this is what powers the MCU during these sleep / wake up cycles.
In short, with OTC the flashlight and it’s MCU is truly off. With OTSM the MCU isn’t off, it’s powered by the cap while it measures off time until either the light is turned on or the cap power runs out. So, you need a cap large enough to power the MCU beyond your maximum desired off time.