Apple ID issues

You cannot change your email for your apple ID. You can only get a new apple ID. The email you originally used for apple ID must be the same for both devices and and you need to make sure your devices are registered with apple under the same apple ID. If you make a change then that devices will be purged for several months before it can be assigned to a new apple ID

Um, no.... You can change the primary email address of your Apple ID, unless it is already in use as an Apple ID, in use as that Apple ID's rescue email address, or if you're trying to change it to an @icloud.com, @mac.com or @me.com email address.

Where are you getting your information?

Because here's where I got my information: [Change your Apple ID - Apple Support]

For everything except for Settings > iCloud, you should be able to sign out of the Apple ID that's listed, even if it's wrong.

If your old email address is showing under Settings > iCloud, use this article: [iOS 7: If you're asked for the password to your previous ...]

Do all the steps in order carefully.

In the future, sign out of your Apple ID on all of your devices first before changing the primary email of your Apple ID: [Change your Apple ID - Apple Support]

That's confusing but what it reads is you can add an email or other alias accounts but the actual email you signed up with as your apple id is YOUR actual apple ID and it cannot be changed or merged or otherwise altered. This was a major problem for mobile me people who had to add the ME email to get their iPhone to work with their Apple ID. You cannot change the registration for the serial number either for the devices so easily. That's why when you upgrade your devices Apple won't accept your new devices right away and your old devices have to be cast out and banned for being used with iTunes and apple accounts for a period of time. My apple ID is email@apple.com. I cannot ever change that. I can add sub accounts or alias accounts for iTunes, etc. But my ID is fixed for life.

If you have a new ID make sure all your devices are reregistered and log out of everything and log back in under the new ID. Review back to my mac setting and router settings and such. if one device is still with the old then it will door stop everything and make you enter your password every time. Also, your credit card needs to be reaffirmed by every device one time. Its a hassle but it works

An Apple-based primary email address for an Apple ID is set permanently. However, any other Apple ID using a non-Apple email can be changed as described above.

How did you acquire an @apple.com email address? Those should be reserved only for Apple employees. That's why I didn't mention that in my original post.