Each has a different lane:
Software Updater is the actual application that does updating (via apt). You cannot change apt settings from within the application.
Software & Updates is the control panel to change Software Updater's (and other apt-related) settings.
Ubuntu Software is the app store. While you can use it for updating, it won't be automatic. If you do decide to use Ubuntu Software for updating, it will simply hand the job to Software Updater.
Livepatch is a separate kernel-only update service that is independent of apt and deb software packages. It's optional. Using it simply updates your kernel (and nothing else) without requiring a reboot.
1, 2, and 3 work together - think of them as three points of entry to apt: Updating, Settings, and Add/Remove.