If you have the same transfer case as in the first link you listed then it should be a 203. They are big and heavy, and also very strong cases. Normally you have 5 positions on the shifter, starting at the dash and working back:
4 lo lock
4 lo
Neutral
4 hi
4 hi lock
I am trying to remember for sure, but it is either that or reversed, but I think that is the layout. In a 203, unless someone has put a part time kit in, the front and rear are always engaged, and through a 'differential' setup in the transfer case the power is split. They are relatively easy to find, and you could swap one in if you don't feel comfortable attempting to tear down and diagnose your current unit.
Getting into swapping to a 205 on yours is going to be a pretty major undertaking. You are also looking at some pretty good expense involved. So the question is, and think seriously about it, what do you want to do with the truck? What year truck are we talking about?
If you have hubs up front you can unlock, and the 203 still moves the truck with the hubs unlocked, someone has probably put a part time kit into the 203 to allow 2 wheel drive operation. This basically replaces some gears in the transfer case to allow the power to go to the rear driveline when the front is unlocked at the hubs. In that case, finding another 203 will mean either finding one with a part time kit installed already, installing a part time kit in a normal replacement 203, or diagnosing yours. Everyone here can help you if you want to attempt to diagnose the transfer case. It may be something simple that you can do quickly, and it will save you money in the long run to fix what is broke rather than just swapping parts.