Mobile web involves accessing websites via smartphones and tablets. It is an entirely distinct media. A smartphone is a mobile phone that includes numerous functions such as accessing Internet, downloading and using apps, checking email, and incorporates elements such as GPS and camera, etc.
Mobile web apps are web apps optimized for a good phone experience. They aren't mobile applications, but websites written in HTML/CSS and run by a browser. While they may be designed to resemble the feel of smartphone apps, they don't have much in common.