SAS Studio can be implemented in a variety of ways.
SAS UE uses a local installation that's accessed via your web browser and is on a local virtual machine.
SAS Academics On Demand accesses a server installation that's not hosted on your machine - it's hosted via SAS. Which means you can access your files and the software anywhere you have a reliable web browser.
And you can use SAS Studio to connect to your own servers if you like.