In movies of the 1930s and 1940s, upper-class homes had living rooms with walls that had rectangles of molding on the walls, with chair rails. Often, they were painted in contrasting colors. This wall treatment is rarely seen today, but I like it. Is there a name for it?
Are you talking about wainscoting? Or lincrusta?
If you mean wood wall panels from the floor baseboard up to the chair rail. That is Wainscoting. Many different styles and types.
Given the chair rail reference, wainscoting is almost certainly the answer. In particular, the OP seems to be talking about paneled wainscoting, since it can be made of almost any material. Contrary to what the OP says, though, it’s pretty common in higher end homes even today.
Personally I associated dark stained wainscot to the 1930’s time frame.
The recent installed ones that I see are all lighter colors.
It’s called wall frame molding, or picture frame molding, and it’s usually installed under the chair rail.
Like this.
It’s called wainscoting. From your link: “…creating the look of wainscoting…”
While I agree it’s more likely the former, note that lincrusta with dado rails (chair rails) is also a thing.
It depends on if the OP was using molding in the correct technical sense or in a looser sense just to mean “molded pattern”
I had to google what “chair rails” are. Why are they called that?
So when you back up your chair into the wall by accident it hits the raised chair rail instead of denting the wall.
The specific detail of the rectangular boxes created with molding, is call picture frame molding. Do a google image search for picture frame molding. It is a type of wainscoting, but the OP asked for the name of this specific detail.
Oak Wainscotting was pretty popular back in the 80’s and 90’s (along with salmon paint and stucco, and brass look hardware). I restore water damaged wainscoting several times a year. It was usually installed cheaply and personally I think it looks like crap anyway.