Apparently not! Look at both your pics again . The second one is different and I believe INCORRECT. I thought brown was always tail lamps as in the first one.
I guess as long as you pay attention to pin location and not wire color you will be OK.
Excellent advice. We're lucky there's a standard pin shape and location for the 7-pin units. I would never count on the vehicle end to be wired to any RV industry standard color code.