What is the difference in command-line "sudo apt-get update" and using Synaptic or Auto-updater?

sudo apt-get update is run automatically in the back ground regularly. Auto-updater is the same as sudo apt-get upgrade. The pretty gui's use libraries that implement the same functions (they may be the same libraries), it's just a pretty gui for users to use. If you ask it to show you the details you'll notice they are just a slightly massaged version of the console output of apt-get.