GCC, you are quite correct. I was using the derivative in the sense of "copied or adapted from others; lacking originality". The dash 80 after all was the prototype for both product lines. The lineage of the 720 would seem to infer that even within Boeing at some level there was a "derivative" mentality of the two product lines. The Boeing web site says "
The 720 was a short-range, high-performance version of the 707 and was first marketed to the airlines as the model 707-020. United Airlines was very interested in the 707-020 but had previously decided to go with Douglas and the DC-8. To help United avoid any negative public relations for going back to the 707, Boeing changed the name of the 707-020 to the 720." The 720 was in fact structually and aerodynamically different than the 707 and after initially gaining the 707-020 designation became the 717-020 because the fuselage was returned to the length of the tanker (717/KC-135). It then came to be known as the 720 for the reason stated re United.
The confusion that exists and how we relate to these aircraft is shown in MrBernoulli's post.
C135 'Stratolifter', the military transport version of the 707
As he says the Stratolifter was the military transport version of the 717/KC-135, not the 707. The military transport version of the 707 was the -137.