Hi BD, The Flash Player term applies to all browsers that is supported. If you see Flash Player ActiveX in your Add/Remove or Programs and Features, this indicates you have it Installed in Internet Explorer. If you see Flash Player plug-in listed there, it indicates that you have it Installed in Firefox, Chrome or any other browser that is supported.
In the IE add ons, one would also have the Shockwave Flash Object, the ActiveX Control that works with the Flash files for IE that have been Installed and it must be Enabled.
In the FF or other browsers, one would find the SWF vs 10.0.45.2 (latest version) listed and it must be Enabled. This is the plug-in and yes it is needed.
When Installing Flash Player, you would need to Use IE and Install for that browser. Then if you want Flash Player Installed for Firefox or another browser, then Use that browser and Install Flash Player for all non-IE browsers.
The link for non-IE browsers is here which you would download to your Desktop:
Hope this helps explain it.