In one of the last major versions (I think 11.2) we changed the way we named our plugin so that we could always update to a new version, regardless if the current one was in use. However, after updating, this does mean you need to either open a new browser tab, restart your browser, or in the case of the current version of Firefox (which has a bug that Mozilla will be addressing) possibly restart your system.
For details on how the update system works, please see this FAQ: How does the automatic update feature in Flash Player 11.2 work on Windows?