The keyboard pics are very helpful!

Notice how the are other chords hiding inside
of the extended chords.

For instance, the CM7, and C9 have and Em chords
embedded, in the form of the E,G,B combination.

Also, in the C9, you can see that there is a
G chord as well, which is spelled G,B,D.

I think most of the interest of the extended chords
comes from exactly those "hidden" chords. The CM7
sound is what you get when you hear a C, with an
Em hiding inside. That particular combination of
a major and minor sound is the definition of a
M7 sound.

HTH,
Emmit Sycamore