Is there a difference between the two?

When you hibernate time is saved because the computer immediately logs on to windows while when you turn off whatever program that is running have to end or close therefore requiring you to open them again after restarting the computer. By hibernating, you don't have to do that since the programs are preserved just like how they are before you hibernated.

When you turn off your computer all the data[OS, running application] loaded in ram is erased... But when you hibernate the data loaded in the ram is transfered in the hard disk... And again when you reboot your computer, it loads the data back from hard disk to ram...