Each one differs in the environment in which they are tested and you will lose control over the environment in which application you are testing, while you move from desktop to web applications.
Desktop application runs on personal computers and work stations, so when you test the desktop application you are focusing on a specific environment. You will test complete application broadly in categories like GUI, functionality, Load, and backend i.e DB.
In client server application you have two different components to test. Application is loaded on server machine while the application exe on every client machine. You will test broadly in categories like, GUI on both sides, functionality, Load, client-server interaction, backend. This environment is mostly used in Intranet networks. You are aware of number of clients and servers and their locations in the test scenario.
Web application is a bit different and complex to test as tester don’t have that much control over the application. Application is loaded on the server whose location may or may not be known and no exe is installed on the client machine, you have to test it on different web browsers. Web applications are supposed to be tested on different browsers and OS platforms so broadly Web application is tested mainly for browser compatibility and operating system compatibility, error handling, static pages, backend testing and load testing.