I think phaeton refers to a 4 door open car that has removable posts and roll up windows. At least it did in the thirties!
Actually, this is not true for Chevrolet in the early 1930's anyway. If the car had removable posts and roll up windows, like the 1932 Landau Phaeton or the 1932 Cabriolet, it was a closed car, not an open car. The 1932 "Phaeton" did not have roll up windows or removable posts, but it did have a convertible top. Also, the 1932 "Phaeton" had four doors.
It all depends upon the terminology used by the car manufacturer.

The 1931 specifications i have doesn't list the Landau Pheaton or Cabriolet as closed models, but definitely as Convertible models.
The 5 passenger Phaeton is listed as an Open Model.
And just to throw another spanner in the works, for 1931 Chevrolet also sold a Phaeton Chassis which had no body at all, just all the running gear ,4 fenders. grill , hood, cowl, and open car windshield.
My apologies to all the 4 Cylinder fans that some 6 cylinder information and discussions have found thier way into this forum.