It just doesn't have the rig
if we take a look at the plate, I will assume the black one is model C or D (I don't know what is that called but there is something spacing the tenor section strings which I only see on model C and D) and the white one is model B
am I right?
I really believe they are both model B's. Looking at full side profiles of the 2 pianos, they are the same. The black one is too short to be a D, and C's aren't sold or made by Steinway New York. Since Jon Batiste (the band leader on the Late Show) is a Steinway artist, there's a strong relationship between him, the show, and Steinway. Since Steinway probably provides the piano to the show, it would be a newer model. Since that would be Steinway NY, I doubt it would be a C.
That "spacing in the tenor" your are referring to is commonly called the "horn" in the plate.