The first I recall it was in the 1990s when the American based replica builders, owners, and their fans started using the term in their slang.
1962-1965 you will find all kinds of names in print using one word or combinations of words in different orders that picked up on Shelby, AC Cars, Ford, and Cobra. The name Cobra seemed to be understood universally but as soon as the first specification change in chassis came about anyone requiring parts either from Shelby or AC needed to know the chassis number of what they were working on to get the correct replacement parts. The need to know your chassis number developed very early but it was still just a Cobra.
The confusion in the U.S.A. seemed to start when the first word on the new car got out in public. The new car, the car people call either a 427 Cobra or Cobra 427 these days hit the early Shelby parts book (dated January 15, 1965) list as the Cobra II model. That parts book then called all the old cars (leaf spring cars) Cobra I models. Parts for street and race cars were itemized. Legend says that Mr. Shelby didn't like the Cobra I and II designations so they were eliminated. (The magnesium racing wheels designed and produced specifically for 427 Cobras are marked "COBRA II".) The December 23, 1966 parts book says, "Model Number = Model 1 in the Cobra series indicates the Cobra 289, produced 1963 to 1965." A few lines down is says, "Model 2 in the Cobra series indicates the Cobra 427 produced in 1966." Throughout the rest of the book the terms 289 Cobra and Cobra 289 are both used interchangeably. That is the earliest text that I personally have with the newly coined "289 Cobra" name in it. The last new Cobra was history before this book was printed, old car with new name.
My point, none really other than that many names exist today that all came after the last new leaf spring car was completed. Every few years somebody coins a new name for reasons only they know and that just adds to the confusion.
It use to be that if one owned a Cobra that was self explanatory. Once the flood of looks something like AC Cars made and replica* makers and their products exploded into the world more modifiers were required. Some tried "real Cobra" for a Shelby-AC-Ford product but the replica builders, owners, and fans cried foul. Their cars were just as "real" in the sense that they existed in physical form. The term "original Cobra" developed to mean a car that was a Shelby-AC-Ford product. That more or less became ineffective because of the entangled connections between all the parties playing in the recreation/continuation/whatever cars in the last two decades plus. Now I find I have to say that "I have a car made under the co-operative efforts of Shelby American, AC Cars, and Ford Motor Company in the first quarter of 1964.........." for people to understand it is not any one of dozens of other possibilities. One of the descriptions that gets laughs is one a friend offers for his CSX25XX car. He drives it to many events. Almost no one asks if it is a car 'original'. A few will recognize what it. If someone asks if it is a kit. His answer is yes. If they ask what kind says it was an AC kit assembled by Shelby. He tells me the most common response is something like 'oh' and the clueless questioners walk away.
* The vast majority on non-Cobras/427 Cobras are not actually replicas of anything. Facsimile or characturization might be more accurate descriptive modifiers. There are some cars that could accurately be called replicas. I have seen a very small number that the builders took great care in mimicking original parts, materials, and methods with. The majority tens of thousands are just something that looks generally like 1960s car. The typical modern creation is done by people that do not like or do not want an original 1960s car. The common things they want different are usually (but not limited to)chassis design, suspensions, engines, transmissions, wider track, longer wheel base, different brakes, tougher body, body that super wide wheels and tires will go under, cooler cockpits, easy to find parts, and cheap parts. Hmmm, they like the general look of the old cars and the fame attached to them but they really don't like the original cars. It's like the person you wish to date saying 'sure, I like you but before I go out with you, you must dye your hair, change the cut, get different clothes, loose 20 pounds, get those teeth straighter/whiter/whatever, AND go get a better job so you can spend more on me first'. They just said they didn't like you. Before you get real excited, I have met modern car owners and or builders that love the old cars they just can't afford them. To me they seem to be the very small minority of modern car builders and owners. The market serves the majority. I know a person that owns a CSX24XX car AND a more modern looks something like a 427 Cobra car. He likes both for different reasons.