Debian-based
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Debian GNU/Linux is a distribution that emphasizes free software. It is supported on many hardware platforms. Debian and distributions based on it use the .deb package format and the dpkg package manager
64 Studio-- Attempts to specialize in audio and video production on x86-64 workstations.
AbulÉdu French--. Designed for data processing in educational establishments.
AGNULA --Former DeMuDi for multimedia production
BeatrIX --A compact distribution from the Czech Republic that focuses on providing a user-friendly desktop environment.
Behördendesktop --A Debian-based public Linux distribution developed by the German Federal Office for Information Security.
Knoppix-based
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Knoppix, itself, is based on Debian
Feather Linux --It boots from either a CD or a USB flash drive. Uses Knoppix-based hardware detection and the Fluxbox window manager.
Kaella --The French translation of Knoppix.
Morphix-- A Live CD distribution with different flavours, including GNOME. Used as a base for many other custom live distribution such as Clusterix, PHLAK or Gnix.
Musix --A Knoppix/Debian based distribution, intended for music production, graphic design, audio, video editing, and other tasks. It is built with only free software.
PHLAK-- A Live security distribution based on Morphix
Ubuntu-based
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Ubuntu is a distribution based on Debian. Each has a different release schedule: Debian's release cycle is 2 years, and Ubuntu's is 6 months. Ubuntu's packages are downloaded from Debian, re-packaged with Ubuntu version numbers and integrated to the system with Ubuntu-specific patches as needed. Ubuntu officially only supports 2 computer architectures; Debian, about 10. Ubuntu has two maintenance lines (stable, in development); Debian has several suites (stable, testing, unstable, experimental
Ubuntu Server Edition --An official derivative made for use in servers. Ubuntu Server handles mail, controls printers, acts as a fileserver, can host LAMP and more.
Kubuntu --An official derivative of Ubuntu using KDE instead of the GNOME which is used by default in Ubuntu.
Xubuntu --An official derivative of Ubuntu using Xfce. Xubuntu is intended for use on less-powerful computers or those who seek a highly efficient desktop environment on faster systems, and uses mostly GTK+ applications.
Lubuntu --Lubuntu is a project that is intended to lead to an official derivative of the Ubuntu operating system that is "lighter, less resource hungry and more energy-efficient", using the LXDE desktop environment.
etc etc.........................................
for more based linux versions and comparison @
http://en.wikipedia.org/wiki/List_of_Linux_distributions
http://en.wikipedia.org/wiki/Comparison_of_Linux_distributions