Privacy and security

Originally had iPad tied to my Apple ID. Need to change it to my son's Apple ID. Unfortunately, when I change the ID on the iPad, it also changes on both the iPad and my personal iPhone. The iPad has its own phone number but apparently SIM cards are no longer necessary with Verizon. What is the sequence of steps to fix this so that my iPhone and iPad are not mirroring text messages and my location? Whatever I enter on one device happens on the other. I do not want to delete anything on my iPhone.