Stand-by mode is a low power mode that drastically lowers power consumption. RAM still requires electricity, on account of having this quirk whereby the removal of power results in the loss of it's contents. Chances are since all the programs are in memory it would be a bad move to do otherwise.
hibernate saves the RAM to disk and shuts off the computer. when turned on, instead of going through the normal boot process, it will fill RAM with the hibernation file, and then resume where it was.
How many times will you ask the same questions?
the real question is how many times must we para-phrase previously provided answers...