Yes, they often are designed to use a common platform. But I'm speaking specifically to aerodynamic shapes. The body of a car is relatively easy to change in the design phase even with the same underlying mechanical systems, but I believe they still converge on the same basic aerodynamic shapes.

There are actually quite a lot of possible shapes that don't degrade aerodynamics. If you take a look on the conception of any modern car, you'll see that the original design is always completely different from the one it gets after it's adapted to factory.

You’re probably right, it’s more about aero + production constraints. I don’t think the concept cars use the same constraints, which is why they have to change to get to production. Even if a design looks different and is still aerodynamic it doesn’t mean it can be economically produced without large changes to the production process.

I’ve only worked in body panel stamping in automotive assembly as a controls engineer, so I may be taking a bit out of school here.