[AnotherCat]

So seems to me -

If the application is on the task bar pinned there from either the Start menu or List and there is a shortcut in ProgramData/Microsoft/Windows/Start Menu/Programs then one seems to get a double icon on the task bar when the application is run (for me if that is for either run from task bar or run from the Start menu)

If the same is done but there is no shortcut in that directory then no double icon on the task bar when run.

In a multiple display configuration, if in Task Bar settings one sets "Taskbar where window is open" and the applications window is moved to the other display then the second icon disappears off the main display's taskbar.

If the application is pinned to the Taskbar from the running application there seems (for now, not time tested) to be no second icon produced when the application is run even though there remains a shortcut in ProgramData/Microsoft/Windows/Start Menu/Programs . My remaining wonder is if that will survive an update?? EXTRA EDIT - It does not stick, the second icon returns even if not updated.

This all applies to the several applications I have just tested on.