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 the other devices that you have connected. If you delete a picture on your iPhone, then that picture is deleted at iCloud and on all the other devices.
If you want different pictures on your iPhone than at iCloud, then you must turn off iCloud Photos on your phone, and you can no longer expect new pictures to be transferred.
Alternatively, you can use Optimize Storage on your iPhone. Optimize Storage saves space on your phone by keeping only smaller pictures there, and relying on the full files being kept at iCloud Photos. This way you can quickly scroll through all your pictures, even though they don’t take up so much space. 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 lots of the storage that would be used otherwise. For instance, my iCloud Photos is about 140 GB, but Photos on my phone only uses less than 10% of that-- but I can see all my pictures.