Originally Posted by Old Smokey
vapilot2004 was correct in stating that the B707 was Boeing model No. 707. It went on to become an extremely successful and popular aircraft, and the 7x7 designation continued for the 727, 737, 747 etc. It was 'catchy'. The B717 designation was originally intended bor the 'lightweight' B707, the Boeing 720, but not used (I cannot remember the COMMERCIAL reason why), until Boeing's acquisition of Douglas many decades later, when B717 was used for the latest member of the DC9 dynasty.
Actually I think the 717 was the original company designation given to the narrower body KC-135 tanker airframe, while 707 was given to the passenger airframe. I think the 720 was originally designated 707-020, but they wanted to give the impression that it was a separate aircraft type for marketing purposes (and possibly to please launch customer United).