From Wikipedia: "From the late 1980s onwards, Carroll Shelby (Shelby Automobiles, Inc.) and associated companies have built what are known in the hobby as "Continuation Cars"; Shelby authorized continuations of the original AC-bodied Shelby Cobra series. Produced in Las Vegas, Nevada, these cars retain the general style and appearance of their original 1960s ancestors, but are fitted with modern amenities. Initially the car everyone wanted in a Continuation was a 427 S/C model which was represented in the CSX4000 series. This was meant to continue where the last 427 S/C production left off, at approximately serial number CSX3560 in the 1960s.
The initial CSX4000 series cars were completed from some suposedly left over 1960's chassis new old stock as well as newly manufactured parts. However, all chassis that left AC's are accounted for in their records and there was not a batch left over! Given the value of the vehicle many "extra" cars have appeared over the years, even some sharing the same chassis number. Gradually as the vintage parts supply ran low, newly constructed frames and body panels were obtained from a variety of suppliers. The production of chassis numbers CSX4001 to CSX4999 took roughly 20 years and many different business relationships to complete."
That is consistent with my recollection as to how the "continuation" series came about. Since they were 1960's vintage chassis they were titled as such.
John