You are mixing up two separate functions:
The Photos you see in the Photos app on iCloud.com are photos which are housed in the iCloud Photos Library.
The purpose of the iCloud Photo Library is to share all photos in that library across all devices that are signed into iCloud Photo Library with the same Apple/iCloud ID. It is a syncing/sharing service, and what you do in one place is propagated to all of the other places immediately.
If you do not want to use iCloud Photo Library on your iOS device, then you can import your photos to a computer that does use iCloud Photo Library, and they will be uploaded to iCloud once you have imported them to your computer:
To then get photos back down to your device (other than those on Photo Stream and the Camera Roll), you would sync your device to iTunes on your computer, and select the photos/albums you wanted sync'd back to the device:
You cannot turn iCloud Photo Library on on that device, or everything will be replaced with the entire iCloud Photo Library.
So, you don't "back up" your photos to the iCloud Photo Library. You can do an iCloud Backup of your device, and the photos on that device will be saved in that backup, but they are not accessible. The backup is there so you can restore your device to it if needed. But the backup will only have those photos that were on the device at the time the backup itself was done.
Best of luck,