If you start the updater from the "FSDT Live Update" icon, it automatically quit when it has finished updating what was required to be updated, since the program doesn't have any other features, so once it's done, there's nothing else to do and the only option is to quit, so it quits.
Instead, if you start the updater from the "FSDT Installer" icon, it will give you time to see what's happening and/or decide what to update, and it won't quit at the end.
The actual program is the same ( is the same .EXE ), just running with two different interfaces depending which icon you use to start it. Running the "FSDT Live Update" is functionally identical than running "FSDT Installer" and clicking the "Update ALL" button, the only difference would be the updater will automatically exit at the end.