update-manager | GNOME application that manages software updates | Mehr ...
This is the GNOME software update manager. It checks for updates made available by Debian and third parties running Debian package repositories, and lets the user choose which to install.
update-manager-core | APT update manager core functionality | Mehr ...
This package holds the core functionality for the APT update managers such as update-manager, the GNOME update manager. Update managers are applications that help you keep your system up-to-date by providing a nice interface in which you can see the list of updates and install them using APT.