We apologize if this is confusing. Here is the difference.
First, the device's iCloud backup used when changing phones: even without paying anything, if your device is set to back itself up to iCloud, the data inside this app is backed up together with the rest of the device.
You can use this to carry over the app's data when you switch to a new device.
The paid iCloud Backup feature is something different. Inside the app, it lets you back up just this app's data to your own iCloud, separately from the device backup.
It is a manual backup that you create yourself. It is useful for people who want to make frequent backups of their diary, or who want to transfer or sync data with another device such as an iPad.
Of course, it also works when changing phones and makes the move easy.
To sum up: when changing devices, you can move your data for free using the standard iCloud backup that is already built into your device.
With the paid iCloud Backup feature, you can create backups as often as you like, protecting you against sudden device loss or failure, and letting you back up and restore easily at any time.
Thank you for considering it.