Difference between Google Photos Sync and Google Photos Backup Sync? In the Accounts section of setup, what is the difference between
Google Photos Sync and
Google Photos Backup Sync?

When would I want to enable one over the other, and when would I want to enable both?

Specs:
Moto G 4G, 3rd generation, UK edition
Android 5.1 Lollipop
Google Photos in sync is what synchronizes your photos saved in Google Photos with the device. So if you add a photo on one device, it automatically appears on your other devices. This is only going to use data when photos are added/removed from Google Photos, so it shouldn't really be a concern for the battery unless you're constantly uploading photos to Google Photos from other devices or the computer.

Google Photos Backup is the automatic photo backup feature that uploads your pictures/videos to Google photos automatically. You can disable this, but you have to go into the Google Settings app. In there go to Google Photo Backup and you can turn it off or set it to upload only on wifi or mobile as well, and you can even set it to run the backup only when charging. And this will only be contributing to battery usage while photos are being uploaded, so unless you are taking tons of photos and have them set to upload over mobile or wifi.

Now the decision is yours!