Why is my phone and tablet linked? I never wanted it that way

When I do a search on my tablet or phone the search also shows up on the other device. I do not want that

Welcome to Android Central! It's because the devices are logged into the same Google account. The idea of a Google account is that your information is available on all of your devices that are logged in with that account.

You could create several different accounts and log in to each device with different accounts. But this means you wouldn't be able to share purchased apps between those devices.