I have resolved the issues presented without having to find and uninstall the Macromedia Flash Player 8.0 in order to get "Adobe Flash Player 10" playback of .swf files on my computer. When I begin this task, I expected to download an "Adobe Flash Player 10" as a player program download instead of the Internet Explorer and Firefox plugin that it appears to be.
This is what I did and what I believe I have:
1. I setup Internet Explorer 6 as my default browser and then used the following site to download Adobe Flash Player 10
2. As I had done before (and also suggested in another thread here), I went to Tools/Manage Add Ons and found Shockwave Flash Object, highlighted it, and clicked on Update Active X. Next, what I did not do before, I restarted the computer immediately after that.
3. Next, I set Mozilla Firefox as my default browser and then used the above site to download Adobe Flash Player 10 again.
4. With Firefox, the critical step included Firefox Tools/Options/Content with File Types (Configure how Firefox handles certain types of files) and the Manage Tab there. SWF Shockware Flash Object/Change Action/and dotting "use this plugin" - Shockwave Flash, followed by a computer restart got the job done.
Now, if I want playback of a .swf file, I can
a. Open With Internet Explorer (assumed with the Adobe Flash 10 "plugin")
b. Open With Mozilla Firefox (assumed with the Adobe Flash 10 "plugin")
c. Open With Macromedia Flash Player 8.0
I am satisfied with those results for my use. Any additional comments on the player vs plugin aspect of the matter would be interesting and helpful.