"Turn Off Hard Disk", is poorly worded in the Windows 7 power properties, the drive is put into "standby", not actually turned off. The drive is "spun-down" to save energy and wear on the motor bearings. On supporting laptops it is put in an even lower standby state. Like ranon said, it occurs when the system or a controller/driver deems that the user is idle for disk activity. It is an independent item, for example the hard drive can go to sleep without the screen saver or screen-off occurring.
If the drive is accessed, the drive wakes back up, The motor spins the platters back up to speed, and then any access to it is returned. You can tell it went to sleep by hearing it spin back up, or because of the seconds of delay you get when trying to do something.
Hibernate is to save the entire present state of operation by moving the ram to disk, and putting the computer into the "off" state.
A computers main Ram needs constant power to keep the Data in it. By shifting the contents of the ram to disk, the contents can be returned to ram. That way even though the ram was empty, the state that the computer was in can be returned mostly. Returning from Hibernate, the contents of the ram are put back in from the hard drive.
"sleep" saves the current state in RAM, "hibernate" saves the current state to hard disk. Both result in the computer being powered down, but "sleep" uses some battery power, but is quicker to power up again. – MrWhite – 2011-10-20T10:46:30.797
@w3d I mean I'm pretty clear about the differences between to sleep and to hibernate, but confused about the RAM and hard disk – Pacerier – 2011-10-20T10:48:38.253
You can't use the computer if your monitor is turned off, and if you shut down the computer the monitor shuts down along with it too. This doesn't mean that turning off the monitor and turning off the computer is the same thing. – Thomas Bonini – 2011-10-20T14:23:35.447
@AndreasBonini ok.. though we can of course use our computers even when the monitor is turned off. – Pacerier – 2011-10-20T14:27:35.623
2You might find live CDs interesting. You can have the entire OS running normally without using the hard drive at all (and if you can manage to cache the entire CD in memory, you could take that out too). – Brendan Long – 2011-10-20T17:32:27.693
I've seen the term "hard disk" used to mean not the hard disk, but the computer box (in contrast to monitor, keyboard, etc). Perhaps that is part of the confusion? (As Dave wrote in his answer.) – Thomas Padron-McCarthy – 2011-10-21T07:30:19.267
@Thomas I guess so it is – Pacerier – 2011-10-22T14:26:44.230