The front end on the red car pictured is definitely Gremlin-based, and almost certainly is the only full-sized styling model constructed . . . and also almost certainly a non-runner (no engine or running gear). It makes sense that AMC would have switched to the larger Hornet base for the actual running prototype car . . . even the light-duty trucking this car (if produced) would likely have been called upon to do called for a slightly larger car than the Gremlin-based styling prototype . . . and, in fact, the running prototype is indeed larger and also differs somewhat in the integration of the bed into the cab. It's more "El Camino" looking, where the red Gremlin-based car looks like exactly what it is - a Gremlin cut off behind the driver's seat with a pickup box stuck on it. I would surmise that AMC had second thoughts as to what market a car/truck like this would most appeal to, and went upscale a bit to go after the El Camino - Ranchero market rather than the light pickup market. Probably more room for heavily-optioned models to generate more profit for AMC (badly needed at that time). This is further borne out by the life of the existing car - it was later retrofitted with the biggest AMC V8, sporty wheels, and eventually a newer Hornet front clip. It ended up looking every bit the muscle-car/pickup that the Chevy El Camino SS-396 was. It's really a shame AMC lacked the resources to pursue this car, it's pretty neat. Certainly better-looking in its final iteration than the Gremlin-based vehicle it started out as.
All just my opinion, of course. Lots of "almost certainlys", "likelys", and "surmises" in there . . . but in answer to your question, the red styling prototype is Gremlin-based, and the actual running prototype was Hornet-based after a quick (and in my opinion, wise) rethink by AMC. Whether or not there was more than one running car eventually built is also a matter of conjecture - it went through so many changes over its lifetime that it's easy to see how folks could see the car twice and not think it was the same vehicle. Adding to the confusion is the fact that at least one "AMC Cowboy" has been re-created on a stock Hornet base in recent years. AMC never built this particular car, but it's pretty well-done and it appears at car shows every once in a while.