If the manufacturer (Plymouth) commissioned somebody else to design and/or build the car, it's a "Plymouth XX-500 by Ghia". If the coachbuilder and/or design house initiate the project, it's the other way around, as in "Ghia XX-500, based upon a 1951 Plymouth".
It seems this car falls into the latter category:
"The first of Plymouth's postwar concept cars was the XX-500, which was built by Ghia in Italy and designed by that firm's Mario Boano and Luigi Segre. Virgil Exner, who had been named chiefof design in 1952, was not involved directly with this one. It was based on the standard 1951 Plymouth chassis with a wheelbase of 118.5 inches and the standard 217.8-cubic-inch, 97-horsepower inline-six under the hood. The gearbox was a three-speed manual.
The XX-500 wasn't a radically designed car. It was tame even by Ghia's standards. The four-door sedan did have smooth rounded lines that were unusual for a car of the era. It resembled Pininfarina's Cisitalia coupé, even though Ghia built the XX-500. Inside, the upholstery was Bedford Cord and leather. The whole car only cost $10,000 to put togeth-er, which was a bargain even in 1951.
"It was brought over by Ghia," Virgil Exner Jr. told Richard Langworth in Special-Interest Autos, "to show Chrysler their ability and craftsmanship and to get Chrysler to give them some business. In retrospect, the XX-500 was pretty dumpy, but it was built along the lines of what they were doing in Italy at the same lime. The design didn't scale up too well, but it started the whole idea in dad's mind that they could do an advanced design and build it as a real car, as opposed to just mock-ups as in this country."
Approval of the XX-500 project inspired Exner Sr. to set up a small staff to create dream cars for Chrysler. The staff consisted of 17 people, including four designers and several model builders."