How to update the system using the terminal?

I normally update my Linux Debian using the Update manager, but how can I do that using the terminal?

On Debian and most Debian-based distributions (including Ubuntu):

Refresh the package database: apt update, apt-get update or aptitude update
Install new packages: apt upgrade, apt-get upgrade, or aptitude safe-upgrade.

apt(-get) upgrade only updates existing packages and is safer, while apt full-upgrade or apt-get dist-upgrade may install new dependencies or remove existing ones.

(See also: apt-get vs aptitude)

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