Gnome, Mate, KDE, LXDE and XFCE are all different Desktop Managers. One must try them to actually see the differences. I'm a fan of KDE, well, it's the most configurable to me. Other folks like the new look of Gnome (Gnome3), because it looks more like a modern day tablet or phone. Mate is a fork of Gnome 2. They forked it because many of the Gnome 2 fans did not like the new look of Gnome 3 (Mate is Gnome 2 unchanged). Cinnamon is another fork of Gnome 2, except that it uses the shell of Gnome 3. Unity is Ubuntu's answer to Gnome 3 and LXDE and XFCE are older, stable (but still improving) lighter desktop managers, and, there are many more.
If you're looking at Ubuntu, as I said before, they feature the Unity desktop. One of the other mods here favours it, as do many of the Ubuntu fans, although many of the older Ubuntu fans didn't like the new look and changed distros. BTW - The reason Ubuntu created Unity was because they didn't like the look of Gnome 3. Mint, which is/was a more user friendly version of Ubuntu, didn't like the new look of Unity, and, started creating their own desktop manager so they wouldn't have to use Unity. They created Cinnamon, which is a cross between Gnome 2 and Gnome 3 with the look and feel of Gnome 2.
Heh, confused yet? Which is the reason I said you have to try them for yourself to see which one you prefer. Live CD's are a good way to get a feel for a distro and their corresponding desktop managers. They run a bit slower than the installed to hard drive version would be, but they are good for testing and getting used to the look and feel.
Most of the different desktop managers have all the features that the others have, and, there's no reason why you couldn't run a Gnome based application in KDE or vice versa. When I switched to Gnome a few years back I used to run a lot of KDE applications with it. When I switched back to KDE, I continued to use some of the Gnome applications that I was comfortable with when I used Gnome.
The nice thing about Linux is you get to choose what you like and include it in the distro you're running. Or, you can choose a distro and then pick and choose the features you like during installation, so, it's not the same as the default version.
If you've looked at Ubuntu and Mint, give their Live CD's a try and see how they feel. I'm running Fedora right now, and, I can download Live CD's in many flavours. The default of Gnome 3, the KDE version, the XFCE version or the LXDE version. Even though Fedora defaults to Gnome 3, I decided to use the KDE version, and I chose that when installing. The install DVD has all the choices in one place, or, you can install directly from the Live CD's of each version.
If you have any other questions, please ask. I hope my answer helped more than it confused, heh.