'Body in white' is a coachbuilding term - bodies start with primer, than a base coat of color - other layers are added from there.
Here's a pretty good explanation for the term
'body in white'.
PS - one other definition of 'body on white' is a bare monocoque in 'white' from the factory with suspension components and not much else, intended for racing. Ford has a decent 'body on white' program for the Mustang.