A custom car is a phrase that became prominent in American pop culture in the 1950s, and has enjoyed special interest popularity since that time. It relates to a passenger vehicle that has been modified to improve its performance by altering or replacing the engine and transmission and to make it look "unique", unlike any car that might have been factory finished,always a personal "styling" statement by the re-styler/re-builder.
A development of hot rodding, the change in name corresponded to the change in the design of the cars that were being modified. The first hot rods were made from pre-WWII cars that had running boards and simple fenders that bent over the wheels. These were modified by removing the running boards and either removing the fenders entirely or replacing them with very light "cycle fenders". The purpose was to put the most powerful engine in the lightest possible frame and body combination. The suspension was usually altered to make the car lower; the front was often made much lower than the rear. Much later some hot rods and custom cars swapped the old solid rear axle for an independent rear axle, often from Jaguar. Only rarely was the grille of one make of car replaced by another; one exception was that the 1937 Buick grille was often put on a Ford. The original hot rods were plainly painted like the Model A Fords from which they had been built up, and only slowly begun to take on colors, and eventually fancy orange-yellow flamed hoods or "candy-like" deep arcylic finishes in the various colors.
With the change in automobile design to encase the wheels in fenders and to extend the hood to the full width of the car, the former practices were no longer possible. In addition, there was tremendous automotive advertising and subsequent public interest in the new models in the 1950s. Hence custom cars came into existence, swapping headlight rings, grilles, bumpers, chrome side strips, and tail lights. The bodies of the cars were changed by cutting through the sheet metal, removing bits to make the car lower, welding it back together, and adding a lot of lead to make the resulting form smooth. By this means, "chopping" made the roof lower; "sectioning" made the body thinner from top to bottom. "Channeling" was cutting notches in the floorpan where the body touches the frame to lower the whole body. Fins were often added from other cars, or made up from sheet steel. But in the custom car culture, if you were someone who merely changed the appearance without improving the performance substantially, you were looked down on.
Paint was an important concern. Once bodywork was done, the cars were painted unusual colors. Transparent but wildly-colored candy-apple paint, which was applied atop a metallic undercoat, and metalflake paint, which adds aluminum glitter within candy-apple paint, appeared in the 1960s. These took many coats to produce a brilliant effect -- which in hot climates had a tendency to flake off. Custom cars also continued the habit of adding decorative paint after the main coat was finished, of flames extending rearward from the front wheels, and of scallops and hand-painted pinstripes of a different color than the rest of the car. The latter, most often being of a single coat, would be expected to be of a simpler paint.