More on the 720
The first designation for the 720 was 707-020 (other 707s were 707-120, 707-320, etc.). The 720 was indeed shorter, but used the same fuselage cross-section but with lighter weight materials in the main structure, the wings, landing gear, etc. It was meant for true domestic short to medium range flights, whereas the earlier 707s were for longer haul domestic (coast to coast) or intercontinental flying.
The 720 was built first without turbofan engines, just like the 707 was. When later versions were fitted with tubrofans, they had the highest power to weight ratio of any Boeing, and may still hold that distinction today, I'm not sure with the 737NGs out there now.
Most observers could not distinguish the difference between a 707 and a 720 - it was easier to tell by tail numbers and airline operators. In the U.S., United, Western, Northwest, Continental and Eastern bought sizeable new fleets, and PanAm bought about 10 second hand. The last major U.S. original operator was Western, who retired theirs in 1980.
720s vanished fairly fast from the late 80s onward. Many were bought by the USAF for engines and spares for the KC-135. Others went to charter and second-tier operators. One of the last operational 720s was just scrapped, very unceremoniously, this past June in Phoenix after serving as an engine testbed (there is a video of it on Youtube). There are a couple others with Pratt & Whitney, and one VIP aircraft is stored (or was) in Malta I believe.