Telerik.Web.Design.dll - this is the assembly which hosts the Telerik AJAX controls designers. It should be referenced on your development server and is not mandatory to be present on your production server.
Telerik.Web.UI.dll - the assembly which incorporates the source code of the AJAX controls. Mandatory for the development and production servers.
Telerik.Web.UI.xml - the xml schema which contains the VS Intellisense of the Telerik AJAX controls. Recommended for the development server, optional for the production server.
the Telerik team