The same processes can run locally on the desktop or remotely on the server. The desktop option is only enabled if Voyager Desktop is installed on the client machine. The server option is only enabled if the license level is Workgroup or higher.
If a process is run on the desktop, the output is accessible directly from the local machine via the "open" link under "Output".

If a process is run on the server, the output is added to a zip file that can be downloaded via the "download" link under "Output".

To run geoprocessing processes on the Server, an ArcGIS Server license must be available.