NOOBS is an easy operating system installer which contains Raspbian. It also provides a selection of alternative operating systems which are then downloaded from the internet and installed.
Raspbian is a free operating system based on Debian GNU/Linux and optimised for the Raspberry Pi hardware (the armhf processor architecture). Raspbian comes with over 35,000 packages, or pre-compiled software bundled in a nice format for easy installation on a Raspberry Pi. The initial build was completed in June of 2012, but the distribution continues to be active developed with an emphasis on improving the stability and performance of as many Debian packages as possible. Although Debian produces a distribution for the arm architecture, it is compatible only with versions later than the one used on the Raspberry Pi (ARMv7-A CPUs and higher vs the Raspberry Pi's ARMv6 CPU).