Internet Explorer, Firefox, and Chrome each use different types of plugins IE uses ActiveX Control components, Firefox uses NPAPI plugins and Chrome is deprecating NPAPI plugins and using PPAPI plugins. It's possible you have the latest version installed for one of these, but not all.
The Flash Player Download Center (http://get.adobe.com/flashplayer) downloads the installer corresponding with the browser you visit the page with. Therefore, if you go there using IE you'll get the Flash Player installer for IE. If go there using Firefox you'll get the Flash Player installer for Firefox. Google embeds Flash Player in Chrome. Ensure you have the latest version of Chrome installed to have the latest version of Flash Player for Chrome installed.