The Linux distribution maintained by the Debian Project that uses the .deb package format is Debian.
Debian is one of the oldest and most influential Linux distributions, with its first release in 1993. It is developed by a worldwide volunteer community under the Debian Project and is known for its broad package collection, emphasis on stability, and support for many hardware architectures. Debian also provides the foundation for several other distributions, including Ubuntu.
The .deb extension identifies Debian software packages. A Debian package is an archive containing metadata, control information, dependencies, installation scripts, and the files that make up the software. The low-level dpkg tool handles individual packages, while APT resolves dependencies and retrieves packages from configured repositories.
Ubuntu is a frequent source of confusion because it also uses .deb packages, but Ubuntu is a separate Debian-derived distribution maintained by Canonical and its community. Arch Linux and Fedora use different primary package formats: Arch uses pacman packages, while Fedora uses RPM packages. The wording “maintained by the Debian Project” therefore points specifically to Debian.