American Motors preserved the early Rambler's tooling, using it as the basis for the Rambler American line introduced for the 1958 model year. This kind of hiatus is rare in automobile history, where the past is discarded and forgotten in the constant drive to entice buyers with something new and presumably better.
Background on Nash Ramblers is here, and on Rambler Americans here.
The images below help to illustrate how American Motors modified the earlier bodies to create the new sub-brand.
This is the Nash Rambler product line for 1953 following a major facelift. All of these cars had a 100-inch (2540 mm) wheelbase.
Country Club hardtop convertibles and other Ramblers were facelifted for 1955. The upper photo shows a 1954 model, the image immediately above is of a '55. The latter received a new grille and (finally! now that George Mason was no longer on the scene) larger front wheel openings.
Four-door sedans and station wagon were introduced in 1954. Their wheelbase was 108 inches (2743 mm), a dimension continued on the redesigned 1956 Rambler line.
Shown in this publicity photo and the preceding one is a 1955 four-door sedan Rambler.
Here is a 1960 Rambler American two-door sedan. It and all other Americans had the 100-inch wheelbase of previous two-door Ramblers. There was no Country Club hardtop, so this model retained the door of the convertible and station wagon shown in the top image. Besides a new top, this model got a new grille and larger rear wheel openings.
A four-door sedan was added to the American line for 1960, as shown in this publicity photo. Unlike the 1954-55 four-door sedans, the wheelbase was 100 inches. That made things a bit cramped, even for the model seen climbing out of the back seat area.
I found no decent images of 1960 American four-door sedans on the Internet aside from the publicity shot above. This photo is of a car for sale. Its top seems to be the same as that of the two-door sedan. To make a four-door version, the front doors were shortened and given a vertical B-pillar. The rear doors are new, of course. To accommodate roll-down rear windows, the aft cut and post are vertical, thereby creating a short six-window sedan (typical six-window U.S. sedans were large, long automobiles).