There must be some difference with Michelin CP tyres but whether it's limited to a different mould with the CP and Camping who knows.
Personally I don't think even Michelin are that cynical and that there probably structural and compound differences.
Certainly the CP tyres have a higher max pressure allowance than basic C tyres.
It is a mystery to me also. There are other details beyond just the rating numbers, such as the the number and types of the radial reinforcement. Say four sets of steel, one of nylon. When I went through it with the ATS man these were also identical between the Michelin and the Tigar, you'll find them marked on the side, but who knows how they are actually laid up, what the materials and gauges used are, what the rubber compounding is, they appeared to be identical, from the same mould, but could be completely different inside. One built to a price point, the other with the finest stuff. Or they could be identical, supplied to different markets, under different brand names to avoid competing within the same business ownership and expanding their market.
Actually Michelin invented radial construction in 1946, using steel belts, which was revolutionary, we all drove on crossply tyres before that and still did long after, until presumably the patents expired. A Michelin X was then a premium product, unquestionably superior, and priced accordingly.
I'm sure that Michelin still know their stuff, and if they have said that a specific tyre is not recommended on a camper they may have their reasons, either marketing, or actual engineering. But if they won't say why, and they won't, I remain skeptical. I truly see no difference between a camper and a commercial vehicle, except that the commercial vehicle may see far more arduous service than a camper. Sure, many just run around doing e.g. parcel deliveries, but others do run fully loaded, even over-loaded, doing vast mileages. And don't require some sort of specialist tyre.
I run mine at the pressures that Dethleffs specify and have placed on a clear label inside the door, along with a reminder of the plated and individual axle weights, 60 psi front, 65 (max) at the rear, and that is in accordance with what I understand about how things work, and the load rating, which is close to what my loaded van runs at, from my actual weighbridge measurements. AFAIK the load rating is only valid at max. pressure and should be de-rated below that. Makes sense to me.
Certainly on our cars the specified load rating for the tyres is far in excess of what could possibly be achieved under any circumstance, and they run at pressures far below the maximum for the tyre. Whereas my camper weighs nearly as much as a modest car at each corner, and has physically smaller tyres than ours.
Though I've seen other discussions where people suggest far lower pressures, but I'm not sure why they would want to do that, and I wouldn't want to have to argue with the insurer if say an accident investigation determined that they were way under-inflated.
You must also be careful about the tyre valves, you need the proper ones which are solidly reinforced throughout, not the rubbery ones used on cars which can blow out at these pressures. Disaster. Fortunately I spotted that error when mine were fitted, and I think the young fitter probably received some re-education from the manager after that had been corrected. He'd just picked the standard ones from the box, rather than the proper ones, which they did have, along with a heavy duty tool to fit them, they can be a pig to change. I do hope that was the first and last time he made that mistake.
There can be real disasters when they get it wrong, ISTR that Ford in the USA were nearly bankrupted by a class action and recall over a popular vehicle that had been fitted with incorrect tyres (Firestone ?) as OEM resulting in several fatalities and many other accidents. So even the really big companies can still get it badly wrong.
Look at new motorhomes at shows and see what tyres are fitted as new. How many of them are some secret-sauce specialist camping tyre ? No, they are probably just what the base vehicle manufacturer's buying department chose after negotiations, and entirely adequate. Or not, certainly my Pirellis were not, but perhaps they were simply the lowest bidder. Perhaps the big industry groups of motorhome manufacturers do get to specify what they want for their base vehicles, I don't know.