We usually refer to tongue weight for the weight on the hitch for bumper pull trailers. Whereas Pin weight is the weight on the Gooseneck hitch for GN trailers.

I think there are numerous people who would use the term interchangeable, Meaning the downward weight on any hitch.

Ditto what PH related. The tongue of a BP trailer is somewhat self explainatory. I think the pin weight for a GN is related to the tubular, vertical type of hitch.

The actual weights of the two types of hitches are not directly comparable, with their resulting effects on the truck. The pulling capabilities of a vehicle will change depending on the type of hitch, so things get a little confusing. If a truck has a rating of a BP tongue weight of 500 #s, he could conceivably carry two or even three times that amount with a bed mounted hitch and a GN trailer. The towing weight is what can be pulled, and tongue weights will vary with the various trailers, the installed equippment and how many horses are being hauled.

There are many variables in a towing rig, the truck's capabilities, the trailer's total weight,  the proportion of that weight on the hitch, and the varying amounts of weight that will be loaded into the trailer. There are even further considerations when loading. Many trailers have different axle locations and depending on where, within the trailers the horses are placed, the loads will change the various weights on the hitches differently from one another. When you include the individual types of usage each owner expects, even more differences are added to the question.

That's why when someone asks, "what can I pull or carry?", he will receive answers that will considerably vary. Almost everyone's rig differs from another's, even if the brands of equippment were identical, the loading will differ. It can be a confusing situation to try to establish an exact response to the question. Ultimately it boils down to trial and error, and the best guess possible to start.

A lot of the scales can weigh each axle.  Get the weight for your rear axle with out the trailer hooked and up and drive across the scale with the trailer hooked up.  The difference in the rear axle weight will be the tongue weight.

All the truck stops on the Utah Point of Entry weigh by individual axle.  as you drive across you get a Front axle, rear axle, and trailer axle weights. Add the all together to get the total weight for the rig.