The 82 and 83 Supras had a long cat (17.5 inches).
The 84 was a transition year, some had long cats, some had short ones.
85-86 Supras have the short cat (12 inches).
Exhausts from one length cat to the other won't interchange due to the hangers being in the wrong places. Even if you cut off the hangers and welded them on in the right places, I think the 85-86 system muffler would hit the bumper cover if you tried to fit it on an 82-83 car due to moving the muffler back about 5.5 inches.
Picture it this way... the 85-86 exhaust pipe has an extra 5.5 inches of straight pipe right after the cat before its first bend. This moves all the bends and hangers and muffler back by 5.5 inches.
If you want to interchange exhausts just rework the front of the exhuast to fit the cat. Long exhaust on a short cat car, extend the pipe. Short exhaust on a long cat car cut the pipe and shorten it and reweld flange. All the underbody hangers are in the same spot, and the exhaust downpipe is the same for all years. Just one cat is longer than the other and the 1st section of piping is shorter or longer to match. The short cat is actually pretty close to 12 1/4" long (at least on my car).