APT, the Advanced Package Tool, is the higher-level package manager that most Debian and Ubuntu users interact with through commands like “apt-get install” or “apt install”. Its own manual page describes it as a friendly front end: “apt provides a high-level commandline interface for the package management system” and “is intended as an end user interface” (https://manpages.debian.org/bookworm/apt/apt.8.en.html).
What APT adds over the lower-level dpkg is the ability to find packages, download them over the network, and work out their dependencies automatically. The man page explains that a command such as update will “download package information from all configured sources,” after which other commands “operate on this data to e.g. perform package upgrades or search in and display details about all packages available for installation” (https://manpages.debian.org/bookworm/apt/apt.8.en.html). When you ask APT for one package, it figures out everything else that package needs and installs all of it together.
APT and dpkg form a two-layer system. The Debian FAQ states that APT “relies on dpkg to manage the packages in the system,” and notes that APT itself “does not understand .deb files” but instead works with package names and pulls archives “from a source specified in /etc/apt/sources.list” (https://www.debian.org/doc/manuals/debian-faq/pkgtools.en.html). APT decides what to install and fetches it; dpkg performs the install.
By turning software installation into a single network-aware command that resolves dependencies for you, APT did much to tame “dependency hell” and set the template that nearly every later Linux package tool, including yum on the Red Hat side, would follow.