Flash Player works both as a plugin and as standalone. For Firefox, there's an NPAPI plugin, Opera and Chromium-based browsers use PPAPI plugins and the standalone edition has its own version. So, even if you updated the tool on Firefox, the standalone version might require a separate update.
However, there are also a number of websites that use Flash Player updates as a phishing scheme to get you to install malware on your PC. So, if you're sure that you have the latest Flash Player version for the application that you're currently using, then simply ignore the prompt.