Maybe this will help?
This information applies to the TRUCK rating. Local laws (state, province, country, etc.) may be different, so verify with your local laws.
A "weight distributing hitch" ONLY applies to the rear, frame mounted "bumper" hitch receiver (the hitch below the tailgate). ONLY. The ratings for this, and 'in bed" type hitches are entirely different. They do not cross paths, with regard to the hitch methods/locations, themselves. The rating for the "bumper" hitch is dependent on the hitch hardware itself, and the 12K rating is according to the OEM installed hitch, alone. You can upgrade or downgrade this hardware. However, all other weight ratings still apply. For example, you could replace the OEM hitch with a 14K hitch, and be legal IF other weight ratings are not exceeded.
The same applies to gooseneck and 5th wheel ratings. Your "in bed" hitch ratings are dependent on the hardware rating. For example, if you have a 16K rated gooseneck or 5th wheel hitch installed, the maximum trailer weight will be 16K. Still, all other weight ratings must not be exceeded. If your trailer weighs 16K, and you do not exceed: the truck's GVWR (the total weight rating of the tow vehicle alone), the GAWR's (the rating of each axle), and the GCWR (the rating of the total weight of the tow vehicle and trailer(s) being towed), then it is legal.
GVWR = Gross Vehicle Weight Rating. The maximum weight the vehicle (tow vehicle alone) may weigh. The weight of both axles, combined.
GAWR = Gross Axle Weight Rating. The maximum weight that may be placed on each individual axle. Each axle is rated individually.
GCWR = Gross Combination Weight Rating. The maximum weight of the tow vehicle and trailer(s), combined.
The maximum trailer weight, according to the manufacturer's documentation IS NOT a declaration. It is ONLY a recommendation, according to a specific vehicle's other ratings, and is typically represented by the ratings of a base model, which is almost always different than an actual vehicle you may be using. They do this for marketing and baseline statements. Any original or aftermarket equipment added (including the hitch, fuel, passengers, dust, etc.) are not included in this claim. The ONLY way to determine your actual weight ability is to scale it. Anything short of getting the rig on the scale is only a guess. :compute: