What's the difference between Debian Standard and Gnome?

Debian Live Standard is Debian without the Graphical User Interface.

Debian Live Gnome is Debian Standard with Gnome.

TLDR; see Ivan's answer below https://unix.stackexchange.com/a/203328/25985

People coming from monolithic mainstream OS's like windows or OSX are often confused by the heterogeneous nature of GNU/Linux.

By "heterogeneous" vs. "monolithic" I mean that while windows and OSX are both essentially gigantic, singular pieces of integrated software, linux is a collection of pieces and often one piece can be interchanged with a different, parallel piece. Thus the final product varies a great deal; it is easy to end up with a system that may be completely unrecognizable to another linux user.

The formal name of the OS is actually GNU/Linux because "linux" is just the kernel (below, I use small l "linux" in the colloquial sense and capital L "Linux" to refer to just the kernel). The fundamental userspace (native libraries, common unix tools) is a completely separate project usable with various unix-like kernels, including Linux, although Linux is by far the most popular one. So first, beware of these two distinct, independent organizations:

  • The Linux Foundation, responsible for the kernel.
  • GNU, responsible for the fundamental userland. GNU is (or was, originally) also the umbrella for GNOME.

Both the GNU stuff and the Linux kernel are publicly distributed as source code. However, that's not much good to most people unless it is compiled into binary executable form. Because that is a complex task, various pre-compiled GNU/Linux distributions exist, of which Debian is one. Point being, Debian doesn't actually write most of the software in the distribution -- the GNU and Linux crew did.

Distributions generally contain a lot more software than the kernel and fundamental userspace, however. For example, the basic layer of the graphical desktop used on linux is the Xorg server. Xorg is another independent organization, and X is also used on other (unix-like) operating systems. X itself is a sort of minimal, behind-the-scenes entity from a user perspective. It does not provide snazzy widget sets, etc; these come from a window manager (WM) and, optionally, a desktop environment (DE).

There are a variety of DE's available for use with X on linux. GNOME is one of them, and it is the default used by Debian for distributions that come with a GUI. Note that you don't have to use GNOME with Debian, you could also use one of the other available DEs (and/or WMs).

So, to answer your question more specifically:

Isn't Debian under Gnome by default ?

No. Debian is an independent organization, and Gnome is a project maintained by GNU, a separate independent organization. Your version of Gnome was compiled from the GNU source code by Debian.

I was looking at the directory
There you can find the following files for Gnome version
- debian-live-7.8.0-amd64-gnome-desktop.iso
- debian-live-7.8.0-amd64-gnome-desktop.iso.contents
- debian-live-7.8.0-amd64-gnome-desktop.iso.packages
as well as the equivalent ones for standard version

The .iso file of Gnome is 1.2 GB while the standard .iso is just 461 MB, so Gnome version should contain more things.

Doing a diff between the *.iso.contents files shows, quite surprisingly, no difference.

Doing a diff between the *.iso.packages files shows differences.

My conclusion is that the standard version does not include a desktop environment and is just command line. On the other hand, the Gnome version includes many Gnome packages from Gnome Desktop Environment such as Nautilus, Gedit, Libre Office, etc.