I think that Sleep/Suspend to RAM is just saving session to RAM, therefore entering sleep and restoring very quickly, but in case of total battery drain the session is lost as the machine shuts down by power failure.
In Hibernation, the session data active in RAM is saved on the HDD (I think swap partition is needed for this) and then the machine shuts down completely. When the Linux system is started up again the session is restored from disk with all the open programs. (In case of multi boot, one may chose to use other systems like Windows before going back to the Linux, with no impact on the effectiveness of the hibernation procedure.)
I know that Hybrid-Sleep is an intermediary operation; it doesn't shut down the machine (you cannot for example go to Windows in multi-boot) and the RAM is refreshed (like in "Sleep/Suspend to RAM") while data is also saved to the swap space of the HDD.
In case of total battery drain when the machine shuts down completely: what happens with the hybrid-sleep state? I think the RAM data is lost, but is the HDD backup restored when the Linux system is started again?