Several answers!
As Ingo2711 says, you can not partially store your pictures at iCloud Photos. It's all or nothing. I'm guessing that you must have been using the "Optimize Storage" to give your previous phone more room, but even then, the pictures on the phone are exactly the same as the pictures at iCloud, just smaller.
As azaksalmarzur28 suggests, if you want the full sized pictures on your phone, then you need to go to Settings>[name]>iCloud>Photos and change from Optimize to Download. After a while, the original full sized images will be loaded on to your phone. It's a little hard to know for sure exactly when this has happens, and it could be a very long time. But as long as you have iCloud turned on, even after they're downloaded, they will still be on iCloud taking up space there, as Ingo2711 said.
So, to move all your pictures from iCloud Photos to your phone, you should Turn Off iCloud Photos. If you do that, you will get a warning:

If you choose "Download" from here, then the full pictures will be downloaded to your phone, and then iCloud Photos will be canceled. This can still take quite awhile. If you want faster syncing you should find good wifi, plug the phone in, and leave it alone.
What do you think? Will this work for you?