How much work actually happens on SSMS and how much on the server itself?
The SQL Server Management Studio only sends the query (or T-SQL prodcedure) to the server and waits for the result.

There's a difference between running it from LAN or directly on the server ONLY because results has to be transferred on your PC (so the difference is only the time to transfer data on LAN).
(Also, in the first case, your PC has to be turned on for the entire duration of the query.)