This page catalogues operating systems used for personal robots.
"Raspian", a portmanteau of "Raspberry" and "Debian", was the original Linux-based OS for the Raspberry Pi. The current version is still Debian-based, but has been renamed as "Raspberry Pi OS".
To install the Raspberry Pi OS, it is copied onto an SD card using an application like the balenaEtcher or the preferred method, a cross-platform desktop application called the Raspberry Pi Imager, a free download from the Raspberry Pi OS home page. You basically select an image file, select a drive to copy to, then push a button. Done. Then the first time you boot with the SD card you go through an interactive configuration process.
See: Installing operating system images from the Raspberry Pi Foundation
The default Raspberry Pi OS (including all historical versions of Raspbian) has been 32 bit but in late 2020 the beta version of the 64 bit OS became available.
To determine which is running on a Pi type:
% uname -mIf it responds with "aarch64" then it is 64 bit. If it responds with "armv7l" then it is 32 bit.