Separating Apple IDs for iPhone and iPad

You could also disable iCloud Photos and other iCloud services like calendar and contacts, for example, on your iPad in the settings for iCloud, and keep on using the existing Apple Account.

Or erase it completely and create a new Apple Account and then use Family Sharing, in case you want to use app you already bought on your iPad.

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Family Sharing - Apple

Preparing your iPad for the use with a different Apple Account is described in this article:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

After that you can set it up and use it with a different Apple Account.

A backup of your iPad does not include photos, if you sync your photos with iCloud Photos.

This is why backing up photos is necessary in any case.

What does iCloud back up? - Apple Support

Archive or make copies of the information you store in iCloud - Apple Support

Unless you use a different Apple Account, both the iPad and iPhone will share the same iCloud. In that situation at least one of the devices would have to have iCloud photo syncing always disabled or else the photos will eventually also end up in iCloud and then onto the other device. Turning it on and off on different devices won't work because iCloud will just make sure that everything it has in it gets transferred to the device that has iClloud active for that service.

Change which apps sync and store data with iCloud - Apple Support

If you do use two accounts it is basically like having a separate persona. Typically somebody might want to do that if they have a business-only phone and a home-only phone.

If both devices have that service signed into iCloud then what you do on one is done on the other too. If you deactivate photo syncing on the iPhone first, you can then delete the photos on the iPhone. Having disconnected the iPhone from iCloud means iCloud has no idea what you are doing with photos on the iPhone and will continue to work with just the iPad. However, if the photos are in iCloud and after you delete them from the iPhone you then turn on syncing again on the iPhone then my understanding is the photos will reappear on the iPhone. Unless you set up entirely two different accounts you're going to have to permanently turn off syncing (this can be done on a service by service basis as the article I provided indicates) on at least one of the devices. It depends on what you want configured.

Note that if you have your two devices set up on different accounts we may have another very long conversation in the future about two factor authentication codes.

As a first step, make sure your data has been backed up from iCloud:

Archive or make copies of the information you store in iCloud - Apple Support

If you disable iCloud Photos on the iPad first and then delete the photo, without enabling iCloud Photos again on this device, your photos on your iPhone should be safe.

Another perspective on this is backing up. I use iCloud Photos to sync from my iPhone to my iCloud account. At that stage I drop Apple's syncing from my account to my computer. I sign into my iCloud account using a web browser and save the photos to a folder on my computer that has nothing to do with Photos. In fact I don't use the Photos application on my computer at all. So yes, my photos are backed up, but they are out of the iCloud thing altogether once they are on my computer. I then delete the photos on my iPhone (that's how I manage to get away with only needing the 5GB of storage Apple provides for free, even though I have 4 devices signed into my account).