OFSO,
Not flaming, but the difference is that in Standby, the content of RAM is maintained in RAM (requiring power), while in Hibernation it is written out to disk (the hiberfil.sys file) and the system powered down completely. Thus Standby on battery power is time limited, while hibernation is not.
That's the theory - in practice hibernation still draws some power, and standby has been improved to draw less and less power, to the point that the difference in power draw now is not that large. However, hibernation is "fail-safe" in that RAM has been saved to disk, so that if the battery runs out you have not lost anything.
SD