Sleep is a state where the computer will still need a small amount of power to save its state - so when you start again, it resumes at where you left it.
Hibernate is a state where information of your laptop state is SAVED into the HDD and then it will go into hibernate state and no longer requires power until you re-start the machine. In which it will read the hibernation state, reload everything, and resumes at where you left it.
BOTH process requires TIME for the laptop/windows to prepare itself to enter either Sleep or Hibernate State. Sleep state is a lot faster compared to Hibernate, but sleep NEED power (even a tiny amount) to keep that sleep state.
If you got "accidental" power unplug - and no battery - it will go down.
If you still have your old dying battery (battery that maybe last 5-10 minutes) - THAT could be your savior. That amount of time MAYBE enough for the laptop to enter either sleep or hibernate. The idea is that you lose power (cable unplugged) - your dying battery tell windows "I only got 5%" - Windows initiate sleep / hibernate process. In the time, hopefully you have enough time to replug the cable. You will still need to let Windows complete the Sleep/Hibernate process, but at least you won't lose data.
Hope this helps.