The Microsoft Dynamics GP web client provides access to Microsoft Dynamics GP through the Internet Explorer web browser. The user experience and functionality provided by the Microsoft Dynamics GP web client closely matches the experience of using the Microsoft Dynamics GP desktop client. No client application software is installed on the user’s local system. The Microsoft Dynamics GP application process for the user is running on a separate server. A Silverlight 5 application running inside the web browser on the user’s computer presents the application.
The Citrix Client is a application that provides access to a Windows session running on a high-performance Citrix server. Once the connection to the Citrix server is established, you can access Windows applications and work with files in a similar way to working on a local PC. Because the Windows applications are running remotely on a Citrix server you get excellent performance, even on a low-performance workstation.
Note: I have posted above information based on the Web client installation document and Citrix client documents.
Hope this helps!!!