Do I have GNOME or Unity?
Solution 1:
Here a picture of unity desktop:
and here a picture of gnome desktop:
I think you will be able to recognise which of the two is your desktop.
Solution 2:
Screenshot your desktop and we can tell you what version at-a-glance you're running.
If you're running plain old standard Ubuntu 15.04, then you'll have some GNOME components, but you're using Unity.
If you're running Ubuntu GNOME 15.04, then you're using the GNOME environment. This is a specialized variant, though, which has GNOME as the primary desktop environment and not Unity. (It's a different installer ISO as well)
Solution 3:
Unless you have manually changed it, you should be running Unity. The only Gnome update which i read that will be applied is on the Software Center, removing the Unity one