You don't install a live system, you just boot and use it. On shutdown, nothing is changed on the computer you used, unless you opted to install it during the live session.
You can use a live system and save data to network drives, even local drives.. but by default a live system runs in memory only, so all changes/saves by default are lost on reboot, unless you navigate & purposely save them to media that isn't in RAM
Also desktop or server; it's still a live system
Ubuntu Server historically wasn't available on live media requiring installation before you could try or use it, it's not available using the great live media that allows you to fix problems using it :)