MacBook apps appearing on a second MacBook Doc

I have two MacBookPros. Recently an open program from one computer began appearing in the Doc of the other. If Safari is open on the first computer a Safari Icon shows on the Doc of the second computer. Clicking on the icon in the second computer opens the screen content of the first. Opening Mail or any other app produces the same result. The same result cannot be produced in the other direction. Turning off Bluetooth in either computer disconnects the process. None of the selections are checked in Sharing and I do not believe the link is a result of AirDrop.

Here is the display as it appears on the second computer.

Perhaps it is something obvious that I have missed but any suggestions would surely help

Steve