The differences Graybeard listed about covers it. Most trap guns have a raised comb on the stock, sometimes adjustable. Some have adjustable butt pads to help tailor the fit. The ribs on most trap barrels are raised so they shoot at a higher POI. Some trap barrels are overbored and have lengthened forcing cones.
On many of the field grade auto's, they are set up to run heavy field loads, and won't cycle light target loads. Using heavy loads in some trap guns can lead to frame battering. Most Trap pumps and autos are chambered for 2 3/4" shells.
I have an 870 TB Trap gun as well. Mine has the field type stock without the raised comb. It has TARGET stamped on the left side of the barrel, and the barrel is 30" and has the raised "step" rib. The 870 trap guns came with both field and monte carlo stocks, and with either raised or step ribs. Kinda hard to tell the 870's apart unless it says TA, TB, TC, or Trap on the reciever. Even so, any 870 can be a fine trap gun.