The wheels of a pioneer wagon had to be sturdy and thicker than the “gussied up” slender wheels of the surrey and other “city” coaches. The springs and body had to be tougher and were built for rugged off-trail use.
They ventured out onto open territory much like a modern SUV.
(You so rarely see a Corvette blazing a new trail across rut filled wild lands.)
That being said I am sure that there was personalization beyond the whitewashed “Oregon or Bust”
Stage wagons also were built tough with thicker wheels but usually ventured on established routes so more grace was taken with the design. They wanted a bit more personal comfort for passenger trade. They had different paint jobs from plain to fancy.
Here is an interesting source.
The stage coach in the images was a Hollywood prop and is not authentic but the freight wagon is.