To Sync (synchronise) is the procedure that takes the changes to the media in your iTunes Library and on your phone and makes the two (iTunes and phone) have the same information. It's primarily concerned with music, videos, podcasts and photos.
Using music as an example (although it applies to the other media as well), when you add music to your iTunes Library or make changes to Playlists (on your computer), the next Sync of your iPhone with iTunes will add those changes to the phone. iTunes does the work for you. At the same Sync, changes made on your phone, such as the Play Count of each song, the time last played and crucially, any changes to star ratings of songs will be sent to your Library so that the information in the Library reflects those changes.
A backup is concerned with backing up the configuration of the phone and data from apps, onto your computer, so that you can use that backup to restore information to the phone if the phone has to be Restored. A Restore is an iTunes procedure that erases everything for your device so that you can start again. It should only be used as a last resort.
A backup does not back up the media:
- music and videos in your Library need to be backed up as well, but you have to do this yourself as iTunes does not do this
- photos (pictures) are added from a location on your computer to your iPhone, in a similar way to music. You tell iTunes which folder (of pictures) is to be added to the phone any changes to that folder will be added to the phone at the next Sync. So you need to back up the pictures yourself
- Audiobooks should be treated in the same way as music, it's your responsibility to back up the audiobooks
An iPhone (or any other portable iDevice) is not a backup for your computer. Instead, the media on your device is simply a copy of some, or perhaps all, of the content of your iTunes library. You should back up the content of your computer, so that when (or if) the computer's hard drive fails, you have a recent copy of your files.
Photos taken on your phone are in a separate folder on the phone (DCIM folder) and you need to back them up manually. These photos are not copied back to iTunes at a Sync, you have to use your computer's file manager to copy them onto your computer.
With modern iPhones etc., it is now possible to purchase music directly from the iTunes Store, on your device. You need to sign into your iTunes account in your iTunes Library so that the purchases are also in your iTunes Library.