Two devices with the same Apple ID getting each other’s notifications

Hello! I have two devices on the same Apple ID; an iPad and an iPhone. They are completely separate except for the fact that they are both registered under one Apple ID. This has never been a problem, and messages sent on one device would only sync with itself.

However, recently I got a notification on the iPad about adding the phone number to my account or something. Unfortunately I wasn’t paying much attention and clicked ‘yes’. Now whenever a text is sent on one device, it shows up on the other as coming from the second device.

It may seem silly, but it’s important for me to keep these separate (the iPad is more casual, while I use my phone for work). I have looked everywhere to try to fix it, and I can’t find anything.

The most frustrating part about this is that the wayward text doesn’t show up on a separate conversation; it inserts it into an existing one, or (I think- this whole befuddle just happened, so I’m not entirely sure) pulls a conversation from one device to the other. This is more of a problem with the iPad, as the texts I send there are more private, to family and friends, and I don’t want them appearing on my phone.

If that makes sense, and if anyone can help, I would really appreciate it!

Thanks.