Disabling iPhone syncing for personal and work devices

I just need to stop the phones from sinking, and I’m not sure where to turn the feature off. The phones are in close proximity, often, especially in my purse, at my desk, or on my bedside. This is causing a problem with Messages, particularly in groups that I send on my personal phone and the response comes on my work phone. I need to turn it off so that I don’t have to worry about the phones connecting between personal and business

[Re-Titled by Moderator]