What is the difference between backing up and syncing an iPad/iPod/iPhone? What is the difference between synchronizing an iPad/iPod/iPhone compared to backing it up? Is it not the same thing?
A backup it part of a sync.  Synchronizing your iPhone:


Saves a backup of the installed apps and all personal data (contacts, saved games, documents, etc.)
Adds or removes music, podcasts, etc.
Copies the latest version of apps to or from your iPhone.
(I don't remember the rest of the steps off the top of my head...)


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.