A Mobile Web app is an app accessed over a mobile browser. It can be easily accessed via built-in browsers, such as Safari on iOS and Chrome on Android. They are primarily developed using technologies such as HTML5 or JavaScript, which provide the customization capabilities. So, they are basically served from a server and not stored offline anywhere on the device.
Web apps have a common code base and can be accessed like any typical web app on any device with browsers. For Mobile Web apps, responsive web design is the new standard as they have to cater to devices of different screen sizes and resolutions. Mobile Web apps can also access mobile-specific features, such as dialing a phone number or location-based mapping. Mobile Web apps can only be accessed with a valid network (Wifi/4G/3G/2G).
The following is an example of a mobile app. It's a mobile website of The New York Times and can be opened with any mobile browser. The URL for this is http://mobile.nytimes.com. One can perform the same actions as web, such as browser refresh. The following screenshot shows the same app; it's opened using the Safari app on an iPhone 6 simulator, running iOS 10.1:
The next is an Android emulator running Android 6.0 and has the mobile site of The New York Times opened on the default browser app: