I am reposting this with a different thread name because I now have a
quite different understanding now of what is going on. Although the
CCC interface works somewhat clumsily, when I reinstall CCC version
10.2—each time I reinstall it in fact, I am able to extend my screen
on to the second monitor. I see an icon for screen 1 and a separate
icon for screen 2 as I should and I can control the resolutions of
each monitor independently of the other. When I reboot, no matter what
I do, only the screen 1 icon appears and, although I can clone onto
the second monitor I cannot extend my main monitor desktop onto it.

Coincidentally with every version of CCC I have used in Vista 64 I
have always had to reset the resolution (it defaults to 640 X 480)
after every reboot. Now it is bad enough having to reset the
resolution after every reboot. I would hate to think that I also have
to reinstall CCC after every reboot whenever I want to extend the main
screen onto a second monitor.

I am hoping that this new information may help someone help me
understand and fix what is going on here.

Thanks in advance for any help!