All the numbers certainly can be confusing, but most vehicles can pull a lot more than they can carry.
What that means is you will most likely over fill your TV with your "stuff", before you have to worry about pulling to much weight.
You want to make sure that the TV you buy can carry all the people, dogs, toys, tools, and etc. plus the tongue weight of the loaded TT. This will appear on the door sticker as cargo or payload.
Since payload is a function of the individual vehicle and it's accessories, I suppose there are a few. 1/2 ton TVs with higher rating than other 3/4 ton TVs;
but I have never seen one.
Since the TV dealer has absolutely no idea of how much gear you will be hauling or the cargo capacity of any specific vehicle, they like to promote how much that type of TV can pull.
Whether the TV has the cargo capacity and horses to pull the load is up to you.