What's the difference between a Sync and a Backup?

If you want to be able to restore a new device to look like your current device, you would want to do that from a backup.

You can back up to iCloud or to iTunes. The backups created in those two places are a bit different. If you are a belt and suspenders person, you can back up to both places (I do). Here is a support article that explains the difference in what is backed up. Note that in iTunes, a backup will always have the same content, whereas in an iCloud backup, you control what is actually backed up by selecting what items you want backed up in Settings>iCloud>Storage>Manage Storage, then you click on your device, and once you are viewing the specific device "Manage Storage" screen, you will see the items that can be backed up listed. To add or remove items from the backup, turn them on or off:

About backups in iCloud and iTunes - Apple Support

When you sync a device, what you are doing is connecting that device to your iTunes Libraries. Based on what options you set up for the sync, those items selected will replace whatever is on your device with what you have selected in the Device Profile screens. For example, when you hook up your device to iTunes and click on that device, you will see a sidebar with the various Device Profile screens that you can set up: Summary, Info, Apps, Music, Photos, etc. As you select each of those options, a window will display to the right of the sidebar with the various sync selections for that particular option. So, on the Music Profile screen, you have the option to "Sync All Music" or to "Sync Selected Albums, Songs, Playlists, & Artists". If you select the second option, you then will see the various categories of Albums, Songs, Playlists, & Artists with little checkboxes in front of each item. You can then selectively check the specific ones you want on your device. Once you have set up all of your Device Profile screens to your liking, you then click on Apply or Sync, and whatever you have selected to sync will sync to your device, overlaying whatever was there before with the new items you have selected to sync to it. Here is a support article with more detail about syncing using iTunes 12 on a Mac and one for Windows:

iTunes 12 for Mac: Sync iPod, iPhone, or iPad

iTunes 12 for Windows: Sync iPod, iPhone, or iPad

So, you would use a backup to create an image of your device at a given point in time for the purpose of using that image to set up a new phone to if ever needed.

You would sync your device to get photo albums, playlists, songs that are ripped from a CD, etc. to your device that can only come from your iTunes Library.

You sync to get the stuff you cannot download (like apps or new music) to your device so it is set up the way you want it set up.

You back up your device to preserve the image of that device once you have it set up to your liking. You continue to back up regularly because that image changes on a daily basis with new messages, photos, etc.

I would recommend that if you have Wifi, you set up automatic iCloud backups. With automatic iCloud backups, your device will back up to iCloud any time it is plugged into a power source, is on the Slide to Unlock screen, and is connected to Wifi. When I got my new iPhone, I used the iCloud backup from my old iPhone to set it up. It looked exactly like my old iPhone once the set up was complete.

The final piece in all of this is iCloud syncing. If you have an iCloud account, and you have turned on Contacts, Calendar, Notes, etc. (the items listed when you go to Settings>iCloud), those things are all stored in your iCloud account. For those items, neither a backup nor a sync will restore them. What restores those to your device is the simple act of signing back into that iCloud account with the same iCloud ID and turning on those options. They will automatically push back to your device once you are signed on and on a Wifi connection.

Also, if you have turned on iCloud Drive, that will store and sync documents via iCloud, and if you turn on iCloud Photo Library, that will store and sync your photos via iCloud. They work in the same way that the iCloud pieces above work. Once you are signed into the iCloud account and those options are turned on, iCloud will push the data to your device.