The actual software you install is identical to usual (Desktop) Studio One 5 Pro.
The part played by "the cloud" is authorising the software/add-ons/packs. Every 3 days it requires internet access to validate you are subscribed to Sphere still. That's the only difference. No audio processing is performed in the cloud whatsoever.
There's also the cloud storage that you get free, which you use for sharing/backing up files. Quite nice if you use multiple machines.