The Mobile Internet is quite simply a name given to the Internet when you access it from a mobile device, like a smartphone or a tablet. It's essentially the same Internet you would access from a desktop computer. However, because a smartphone is clearly much different from a desktop computer in both its size and its features many websites have created unique versions that are designed to display better on a mobile device than the traditional website would.
Mobile websites are often referred to as WAP sites. WAP stands for Wireless Application Protocol, which is a standard that is used to guide how the mobile version of a website is designed, created, and displayed. Some mobile websites, including m.MyFOX47.com, have unique device detection capabilities. This means that the mobile website is able to identify not only that you are using a mobile device, but what kind of device you are using. The mobile website is then modified so that it displays in the best format possible for your specific device. One advantage of this is that the mobile website is accessible from a wide variety of mobile devices; there are a LOT of different types of cell phones out there! Another advantage is that the user does not have to download a program to their mobile device in order to view the website. All they need is a data connection and a mobile browser, which is a standard feature that is pre-installed on many phones sold today.
"App" is a short name for application. For the most part an application is about the same thing as a program and is downloaded and installed on your phone. Because each application is designed especially for the device on which it is installed, an app is usually able to offer unique features that take advantage of what that device has to offer. However, this uniqueness also means that an app designed for one type of device or operating system (for example, iPhone's iOS) will not work on another (for example, an Android phone) and a separate app needs to be developed. Apps often have many features that will work based on the information stored on the device, however some parts may require a connection to the Internet in order to provide updates. This is especially true for most apps from news organizations as their primary content is constantly being updated.