Raspbian is a family of GNU/Linux operating systems derived from Debian. Version numbering follows that of Debian and the current stable is 10 (Buster). Raspbian is the most widely used Pi based distro and the one recommended by the Foundation, who distribute their own customised images.

Raspbian is a GNU/Linux operating system derived from Debian, which has been around for more than two decades. The current stable is 10 (Buster). Raspbian is the most widely used Pi based distro and the one recommended by the Raspberry Pi Foundation, who distribute their own images of it in several flavors, a full version with a graphical desktop environment and recommended software, a basic GUI desktop, and a "lite" version without any GUI pre-installed. However, all versions use the same repository and it is possible to install a GUI on the lite version and add some or all recommended software to the desktop version.

https://www.raspberrypi.org/downloads/raspbian/

Raspbian runs on all models and includes appropriate kernels for such. The repository provides more than 35,000 binary packages that can be installed using apt-get and other related Debian style tools.

Beware that while Raspbian packages use the armhf suffix, they are not the same as Debian's armhf port, which targets ARMv7 (and so can only be used on the Pi 2 or 3).

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