Freeing up space · Stopping, undoing and apps in the way
What does Ask it to quit do — will I lose unsaved work?
Short answer: It sends the same polite request as choosing Quit from the app's menu, so the app can save and close normally, then confirms it really exited. It's never a forced kill.
It sends the app the same polite request as choosing Quit from its own menu, so the app gets to save and close normally — if it has unsaved changes, it will ask you about them as usual. Storage Studio then confirms the app really exited rather than assuming it did.
Ask all to quit does the same for every app in the way. It's never a forced kill. Afterwards, Storage Studio offers to reopen each app it closed for you — see reopening closed apps.