General Motors launched its all-steel "Turret Top" bodies on much of its 1936 line, as this link indicates. The Turret Top design was strongly rounded, in part because the large, one-piece top stampings were intended to be stackable, and also because GM engineers thought that the shape would lessen acoustical "drumming." (Previous tops had center sections with treated canvas inserts that dampened structure-related noise.)
Since the all-steel cars had rounded shapes, styling boss Harley Earl must have felt that having rounded windows would enhance the theme. But the resulting designs seemed too soft-looking, and GM hurriedly tried to counteract the bloated effect in its 1937 models. The basic body shapes could not be easily changed, but other parts such as hoods, grilles and fenders could be altered, and were.
Here is a Buick four-door sedan sporting the rounded look.
This is a two-door Buick from the following model year. Its roof has a slightly different shape than that of the four-door. But note the model year changes. Fenders have more blunted rear ends. The hood extends over the top of the grille, yielding a longer, more squared-off look. The grille has horizontal rather then vertical bars and its shape is now two squared-off panels.
Oldsmobiles also got the Turret Top and a rounded appearance not very different from Buick's
The 1937 facelift also incorporated an extended hood line. Fenders are more squared-off at the rear then those of the '37 Buicks.
Six cylinder and eight cylinder Oldsmobiles each had different grille designs for 1937 (and 1938 as well). Both designs are a crisp contrast to the 1936 "fencer's mask" grille style.