Deciding which version of Facebook to use on your mobile device is not easy. You have two options: Facebook Touch (or Mobile), which runs in a web browser; or the Facebook application, which requires installation.
Facebook mtouch is a browser-based mobile version of the popular Facebook website that has now been superseded. It was Facebook's first attempt to provide a simplified user experience for touch-based mobile devices. It has now been rolled into the m.facebook.com domain.