Keep this in mind: iCloud Photos is a synchronization service. When you engage iCloud Photos on a device, then the Library on that device is kept just the same as the iCloud Photos Library. So, for instance, if you take a picture with your iPhone, it is added to the iPhone's Photos Library, copied to iCloud Photos Library, and then copied to the Photos Library on each of your other devices. If you delete a picture on your iPhone, then that picture is deleted at iCloud and on all the other devices. iCloud makes the pictures in your iPhone Photos Library and at the Photos Library at iCloud.com and on any other connected Libraries all exactly the same.