As far as I know, the 707 was the upgraded 720 alias Dash 80.
Originally the -80 had a fuselage for a 5 abreast configuration, whereas the DC8 had a fuselage for a 6 abreast configuration.
So the -80 fuselage was used for the KC135 and as a smaller 707 version. The 720.
And the real 707 got a fuselage for a 6 abreast layout, so the could compete with the DC8.
In my point of view. Both birds are real nice. Loud and Proud!!!
But isnīt it interesting.
There are so many opinions and stories about the Boeing-designation, but none for the Airbus-toys.
Perhaps the french guys got their designation A3xx from a bottle of nice red wine.
