upgrade upgrade is used to install the newest versions of all packages currently installed on the system from the sources enumerated in /etc/apt/sources.

What does full upgrade do?

full-upgrade (apt-get(8)) performs the function of upgrade but will remove currently installed packages if this is needed to upgrade the system as a whole. … The dist-upgrade command may therefore remove some packages.

What does APT update and upgrade do?

apt-get update updates the list of available packages and their versions, but it does not install or upgrade any packages. apt-get upgrade actually installs newer versions of the packages you have. After updating the lists, the package manager knows about available updates for the software you have installed.