Maybe you already know this, but here's the difference:
Hibernation saves your memory to the hard disk and switches off the PC. When you turn it back on, the memory contents are loaded from hard disk. That means that both putting the PC into hibernation and turning it on again take some time depending on the amount of memory you have.
Standby doesn't turn the PC off, it usually just switches off hard drives and displays, so it has to be powered but the transitions are very fast.