Difference between shutdown ( power off ) and restart ( reboot )
Solution 1:
For the operating system, shutdown and reboot are practically the same thing.
The OS will shut down as usual in both cases. The only difference is the signal sent to the hardware at the very last moment.
To switch off/reboot the computer, the OS will send a special signal to the hardware once it is finished shutting down. It's only this signal which will be different between a reboot and a shutdown.
The way the signal is sent depends on the exact hardware platform. On modern systems it is usually done via ACPI.
Solution 2:
Go to http://en.wikipedia.org/wiki/Booting#Rebooting