RE: What's a Westfalia?
I've never encountered any problems if I refer to my rig as a Class B or Van
Camper, those terms are normally understood.
As for commercial/private RV parks, I've stayed in many (several during a
month long trip last month) and although getting some strange looks I've
never encountered any questions like have been mentioned in this thread,
like curtains or 'self contained?'.  And I've frequently taken 'tent sites'
at State and local cmpgrounds without any trouble.  But this has all been
out west, Washington, Oregon, much of California, and on this last long trip
Montana, Wyoming and South Dakota.

I did encounter something new in RV parks on this trip, no cable TV
available except in 'premium' or full hook up sites.  Ran into that twice or
three times.  But on the positive side, WiFi everywhere I expected.  Also
encountered such things as "You can put both vehicles in one spot, no extra
charge" (I was traveling with a friend that was driving a 23' Class C RV).
And, as expected based on previous experience, we were allowed to double up
in all the Federal campgrounds we stayed in and in most cases no charge for
the second vehicle.  When you combine that with the Senior Pass it makes for
really cheap camping, like $3 a night per vehicle at one place, the
campground at Devils Tower.