In reply to m0unt41n:
> Thanks. I suspect I am getting confused with terminology.
> Yes having the desktop extended across onto the second screen but with just one application there would be good.
> And with the main screen having anything else that was open.
Windows is quite limited. I think you want to extend the desktop. Windows only supports a single desktop (unlike a linux machine) so you have to have the desktop span two screens. You can then move (by dragging) a window to the 2nd screen and maximising it just that screen. The other screen will have the other windows.
I think Windows 10 will bring multiple desktops, which might give you two desktops on different monitors - both with a start button and task bar.