newcomer towing question?

GVWR.....that is the MAX weight truck can weigh with all passengers, any stuff in cab/bed, any tongue weight from trailer etc.

GAWR......that is the MAX weight front or rear axle can have.

Best thing is to load truck up ready to go camping (you/passengers/stuff/fuel) and go get weighed at a CAT scale
Weigh ticket will show how much weight is on front axle, rear axle and total weight.
Compare to your ratings.......then you know how much weight can be added to truck for a trailer.

In your case........probably a 3500#-4000# trailer (GVWR). Figure 12% of trailer GVWR for tongue weight

You don't have much in the way of a tow vehicle so trailer is going to have to be small

It would help a lot if you post exactly what you TV is. But the GVWR is the absolute max the TV can weigh fully loaded with everyone and everything in it, including the hitch weigh of the TT. But don’t use that number in your search for a TT, pulling at or near your max rating will not be a fun experience. There are a number of rating for your TV and you need to meet the "weakest" one. And put little stock in the GCVWR, you'll likely exceed some rating before you ever reach that. And never believe what a salesman tells you what your vehicle is cabable of pulling, instead ask on the forum.

GVWR is Gross Vehicle Weight Rating
GAWR is Gross Axle Weight Rating

So you know the ratings for each axle and the whole vehicle which is clearly not the sum of the two axles. Now you need to find out how much your vehicle actually weighs in order to determine how much capacity is left for people, cargo, and trailer tongue weight. A CAT scale would help with that, as mentioned.

What you can tow is limited based on a number of ratings. It is the lowest of any ratings defined by the vehicle manufacturer that should not be exceeded. More details about your truck would help. Year/model/engine/trans/axle and if 2006+ the as equipped payload per the tire and loading sticker.

Your owners manual should have a chart showing all possible factory configurations including engine options, with or without 4WD, seating capacity, with or without towing package, etc. As part of that each option will list a towing capacity. That does not mean you can tow a trailer up to that weight. It's just one number to factor in, you also need to consider the numbers others have discussed, as well as available payload and limits on the toungue weight of the trailer.

We can help you a lot more if you can tell us what you drive and how it is equipped.