OK, here goes...
Ubuntu - A version of Linux that's generally regarded as being easy-to-use for computer novices (and nerds alike).
Xubuntu - Ubuntu with an X in front of it.
Linux Mint17 - Mint is another Linux distribution. It's very similar to Ubuntu, but designed to look cool & be even easier to use. Recommended for an absolute beginnier.
Linux Mint13 KDE - As above but an older version (13 instead of 17); and using the "K" Desktop Environment (KDE). See below.
Unix - The grand-daddy of them all. Unix appeared sometime during/after 1969, and grew bit by bit into what it is now.
Linux - A "Unix-like" OS, started by Linus Torvalds in the early 1990s, which has become "really really Unix like" over the years.
Mint16 - Like Mint 17, only one version earlier.
Debian - Like Ubuntu, like Mint, Debian is a "distribution". As it happens, both Ubuntu & Mint are based on Debian.
Mint - See above
Gentoo - Another type of distro ("distribution"). No idea about this one.
Redhat - A deeply horrible distribution, best avoided. Unless you're a 'Hatter of course.
Suse - Yet another distribution. I forget what this one prides itself on.
"Yggdrasil" Linux - Another distro I assume.
Katya - I think that was a version of Mint?
cinnamon - Another "desktop environment" See below.
Desktop Environment - this is how you interact with the computer. How it looks, feels, how it responds to the mouse/keyboard, the borders & icons that surround programs, these are all provided by the "desktop environment". There are 4 of major note:
- Gnome - the most popular Linux desktop environment
- KDE - Another Linux one, but generally less popular. Loved by its fans, of course.
- Apple iOS - Yep, Apple Macs have a Desktop Environment too.... as does:
- MS Windows - Windows is just a desktop environment at the end of the day, with an OS jammed on the back of it.