You've got your numbers right... sorta... and your terms that go with the numbers... but they're not the ones used to determine max trailer weight.
Your truck probably has a GVWR of 8800lbs, this is the max truck weight with fluids, people, cargo in the bed, and trailer tongue weight. Let's say your truck has a GCWR (Gross Combined Weight Rating) of 20,000lb. This is truck (wet) and trailer combined. If your truck weighs 7500lb with a full tank of fuel then subtract that from the GVWR and GCWR. The resulting numbers will tell you two things:
GVWR (8800) minus 7500 (curb weight, wet): 1300lb
GCWR (20,000) minus 7500 (curb weight, wet): 12,500lb
The first number, 1300, is how much payload you can haul in the truck. The second number, 12,500, is how much additional weight you can tow. Just to clarify, you can't haul 1300lb AND tow 12,500lb at the same time. By the time you add people (350-400lb) and gear (300lb) that leaves 600lb that you can put on the truck. If you have 10% of the trailer weight on the ball that's 1250lb for a 12,500lb trailer. By the time you add that weight alone to the GVWR you only have 50lb left for people and gear without going over the GVWR. With 600lb of payload left you're limited to towing a 6000lb trailer, assuming 10% tongue weight.
So, to know what you can realistically tow, I'd suggest having your truck weighed at a public scale with a full tank of fuel. This will give you a starting point to figure out how much you can haul and/or tow without going over the factory weight limits. Just because you can tow an 11,000lb trailer and still be under the GCWR doesn't mean you CAN tow an 11,000lb trailer, you have to find out the tongue weight and how much weight people and gear are going to add and make sure that you're within the GCWR and GVWR. Yeah, the maker says you can tow like 16,500lb with the new Rams. What they don't tell you is that in order to do that you have to have the most stripped down model Ram they make in order to be light enough to do it.
Hopefully this makes sense. The math is pretty simple, you just have to know the weights and limits of everything involved. Also keep in mind that the factory specs of your truck might not be what's required in order to haul 20,000lb safely and reliably. You may need the 4. 10 gears for that. I believe your owner's manual lays it out as far as which configurations can haul what.
Hope this helps, good luck!