In Apple parlance, they are not one in the same.
Sync is a specific transfer of selected data (and by that I mean specifically selected data) from your iTunes and Photo Library to an iOS device. So, when you sync, you can sync some of your Photos, Books, Movies, TV Shows, etc. from your two libraries to your device.
Backup is storage of a particular set of selected apps and all of their associated data from your iOS device to iCloud or to iTunes. The actual apps themselves are not backed up, but rather a link to those apps is placed in the backup so that they can be automatically re-downloaded (if restoring from iCloud) or re-applied (if restoring from iTunes) when the restore is done. The Backup ensures that all data associated with those apps is restored. In addition, backups store your Settings, Messages, Ringtones, Visual Voicemail, Homescreen Layout, along with the option to back up Mail, Notes, and Documents and Data.
So, Sync goes from iTunes to iOS device, and Backup goes from iOS device to iCloud or iTunes.
You can then Restore that backup to your iOS device by erasing said device and then setting it up again from the restore. The restore places all backed up info on the device, so when the restore is complete and the apps and media are reapplied, the device looks exactly like the backup that it was restored from.
There is also iCloud syncing, which can include normal iCloud stuff like Contacts, Calendars, Notes, etc. as well as iCloud Photo Library, iCloud Music Library, and iCloud Drive. This type of sync is a two-way sync. Everything is managed by iCloud where the "source" data lives. You can update that source data at the source via iCloud.com, or you can update it via any of your devices or other computers signed into the same iCloud account with those particular features turned on. Updates from a particular device or computer go up to iCloud and then are pushed to all other devices and computers.
And you can have multiple backups stored for your device. They are backed up and distinguished by the date and timestamp. So, you can then select which one you wish to restore from. iTunes stores as many backups as your computer has room for, iCloud stores as many backups as you have iCloud space for. So, you may only have one iCloud backup for a particular device, but you can have 10 backups of that device in iTunes.
That's the difference in this world.
Cheers,
GB