How to stop iPad activity from showing up in the taskbar of my Mac, and vice versa?

So whenever the iPad is being used, whether it's in a related app like iMessage or Safari or something, it'll show up on the left like this.

It also does this on the iPad's taskbar when the Mac is being used. I'm pretty sure there's a way to turn this feature off, as I believe I've found the answer to this once before, but unfortunately can't remember it... Could anyone help me with this please?

Thank you!