First, there are two Flash Players for Windows (three if you count Chrome's PepperFlash plug-in)
ActiveX is for IE - IE needs it because it uses 1993 ActiveX controls for security, which is not really secure at all, and complicates everything you do with IE.
Tha standard plug-in is for Firefox, Opera, Safari and several other lesser known browsers like Maxthon and Seamonkey.
If you use IE and another browser, you nee both, and they both need to be up to date. As Imentioned Chrome has its own which updates through the browser.
To make sure you're up to date for both, download the following:
Also, download these:
You'll need to install Shockwave with the FULL installer for IE too, but there isn't a direct download for it. You'll need to go to: http://get.adobe.com/shockwave/otherversions/ using IE AFTER everything else is done.
Save all the files and close your browser.
Run the uninstallers first (both of them)
Go to: C/Windows/System32
Delete the Macromed folder.
Open your Registry Editor (Start>Run or press the Windows key + R and type 'regedit' [minus the quotes] and click OK)
In the Registry Editor, go to:
Delete the Macromedia folder (Right click and choose "Delete").
HKEY_CURRENT_USER/Software and delete the Macromedia folder there too.
Close the Registry Editor and empty your recycle bin.
Run the Flash Player installers, and then the Shockwave FULL installer you downloaded.
Lastly, open IE and go to: http://get.adobe.com/shockwave/otherversions/ to download and install the Shockwave FULL installer for ActiveX (IE).
For Firefox, I recommend FlashBlock (https://addons.mozilla.org/en-US/firefox/addon/flashblock/) It's prevent ANY Flash content from loading until you allow it manually. It can get to be a pain, but you eventually get used to it.