What is the difference between synchronizing an iPad/iPod/iPhone compared to backing it up? Is it not the same thing?
To expand on Hand-E-Food's answer.
A backup is a complete snapshot off your device at that particular point in the time the backup is made. Not every synchronize causes a backup, and the backup does not contain actual copies of the Apps, Music, Books or Photos stored on your phone. It does however contain all the settings, contacts, calendars, saved games and anything else not handled by the synchronize.
A synchronise copies all Apps, Music, Books and Photos to the phone, and works in conjunction with the backup. When you restore a backup, it will require you to synchronize to retrieve the actual Apps etc.
You can synchronize your phone irrelevant of the backup state, and if you don't restore a back after a reset, you can continue synchronizing items the way you did before the reset, however all your application settings, saved games etc. will be lost and has to be reconfigured and restarted.
A backup it part of a sync. Synchronizing your iPhone:
The backup is useful if your iPhone has to be reset to factory settings or is lost. You can restore your backup to your fresh iPhone and it will reinstall the apps along with all of their data. Without a backup, you would have to manually type in all of contacts, reproduce your documents, and start your games from scratch. You'll still have to restore your music manually, but that's a minor issue.