Q: What is the difference between Sync  and Back Up?

I there anywhere I can verify that everything was saved?

Hi Robert, to my knowledge there is no way to verify what the backup actually contains. You can however verify that a backup exists in one of two ways. The easy one is after the backup go back to iTunes > Preferences > Devices and your backup will appear there with a date. See screenshot:

You can also use Finder or Windows File Manager to find the location of the actual file. On Windows it is located here (look at the path on top, you will have to unhide hidden files). If you need this for a Mac I can post that location as well. Again there is no way to tell what the backup contains, only that it is there in case you need it. So your only choice is to trust the Apple literature as to what is included in the backup. And yes, for you a backup is the way to go.

See this also:

Find and manage your iTunes backups - Apple Support

Best,

Carlos (elcpu)