I wanted to edit my web page (http://www.cominter.com/annonce/QLXannonces.html.) on my smartphone (Samsung galaxy note 2) and my desktop (windows 7) using two different browsers: chrome and Firefox. With chrome, I get the right page but with FireFox I got other pages as you can see from the screen shots below.
Does this mean that google page rendering may change according to the browser used? Any advice or explanation is welcome.
Google takes your search history and browser history into account, this is why you would get different results.
To get the most neutral search results try opening a incognito window in chrome or with firefox open a "Private Window". This can be done on desktop or mobile.