Texas says pretty much the same thing just less words
Trucks registered for more than 12,000 GVWR are considered trucks and not passenger cars. So they're registered for a fee based on GVWR instead of a flat fee.
Dealerships here in Texas are very bad about registering pickup trucks as passenger cars because of the increased cost.
Several people including me and others on this forum have had to preregister and pay the difference to be legal when towing our trailers.