The Boeing 720 was originally designated the 707-20, then the 717-20 before the settled on the 720. This was before they decided they liked the alliteration of the 7X7 format.
The formal designation of the Braniff 720 aircraft was the 720-027. Braniff also operated various marks of the 707, these being the: 707-138B, 707-227 and 707-327C.
Braniff operated both leased and owned versions of the 720. They initially ordered three with options for additional aircraft. Additional 720s were later leased from Aer Lingus airlines (720-048s). A 720-022 also snuck in, I'm not sure where from.
Onyl five 707-227’s were ever built, all for Braniff, but only four entering service. The first plane ship N7071 was lost during a pre-delivery test flight, when the crew became unable to control a “dutch-roll” condition.
Braniff later leased four long-range Boeing 707-138B’s from Australia’s Qantas airline in 1969. The –138B was the short-bodied 707 with the high-frequency antenna mounted on the top vertical stabilizer and a small fin on the underside of the aft fuselage between the horizontal stabilizers.
Braniff Fleet Register