Standby still uses power to keep data in memory, if you disconnect your
mains you loose it.
Hibernate writes the memory content to a file so you can loose power
completly and still start back up in the previous state.

heck, my system seems to not like either one.
Hybernation starts off ok, writes the file, then on wakeup, it hangs
at the sign in screen. no mouse .

stand by,  gets to the desktop, then hangs with no mouse movement.

I think it's a bios issue....or my windows (xp)  is too essoteric to
work....

wessd