APT is an advanced interface to the Debian packaging system. It features complete installation ordering, multiple source capability and several other unique features, see the User’s Guide in /usr/share/doc/apt-doc/guide.html/index.html (you will have to install the apt-doc package).
aptitude is the recommended package manager for Debian GNU/Linux systems. It is a text-based interface to APT using the curses library, and can be used to perform management tasks in a fast and easy way.
Before you can use aptitude, you’ll have to edit the /etc/apt/sources.list file to set it up. If you wish to upgrade to the latest stable version of Debian, you’ll probably want to use a source like this one:
https://http.us.debian.org/debian stable main contrib non-free
You can replace http.us.debian.org with the name of a faster Debian mirror near you. See the mirror list at https://www.debian.org/misc/README.mirrors for more information.
More details on this can be found in the sources.list(8) manual page.
To update your system, run
aptitude update
followed by
aptitude dist-upgrade