iCloud isn't designed as a place to offload pictures. Using iCloud Photos synchronizes your Photos Library with your iCloud Photos Library. Having iCloud Photos turned on makes the pictures in your phone's Library exactly the same as pictures in your Library at iCloud.com.
ChrisBell1 was referring to Optimize Storage, which saves space on your phone by keeping only smaller pictures there, and relying on the full files being kept at iCloud Photos. Then, when you need the full pictures for printing or editing, etc, the phone grabs the full file from iCloud. This is very cool, but it can lead to a slight delay, sometimes. With Optimize Storage, you save maybe 80% of the storage that would be used otherwise. But the pictures you see on the iPhone are still exactly the same as the ones at iCloud.com.
And, by the way, iCloud isn't strictly a backup service, either. "Backup" usually means that you capture files at a moment in time, so if you accidentally mess one up, you can go back to the backup. iCloud Photos constantly synchronizes the Libraries, so that if you accidentally mess up, maybe erasing a picture you didn't intend, then that mistake is immediately transferred to iCloud. There's no going back. So it's good to have a real backup, like an external hard drive, if your pictures are precious to you.
