This is loosely related, take it for what its worth. I've changed fluid in my NV-350 in my Neon R/T 4 or 5 times. Yea, overkill maintenance.
I used the Mopar Specified Fluid the first couple of times, and since I've used Redline MTL. (Smaller car, thinner fluid). Fresh fluid seemed to make the trans shift better in all gears, but a couple thousand miles down the road, the trans goes back to the slightest notchy-ness during shifting. Only difference I noticed between the Mopar and Redline Fluid, is Mopar, lower gears were a tad notchy, Redline the higher gears were a tad notchy. Obviously, different trans and different fluids, so your results will most likely vary, maybe greatly.
Trans are often very finicky about their fluid, the fluid is sometimes specifically formulated with special properties the trans needs. So the safest fluid to use would be the Mopar specific fluid, make sure you get the exact part number needed. But Redline has an excellent Rep, I have never heard anyone say that their trans performed worse after putting Redline in it, including myself. Redline, while rather expensive, is still cheaper than the Mopar Fluid.
Syncrhos, LSD clutches, Automatic Trans clutches and bands all need to apply friction to make the trans work correctly. Regular Gear Lube, Motor Oil, etc is often too slippery and doesn't let those friction surfaces engage properly. That burns up those friction surfaces, as well causes the device to work improperly, i.e. bad shifting, chirping and grabbing rear ends, etc. The Fluid for these things need some sort of friction Modifier, and they are needed at various levels.
ATF has Friction Modifiers in it, and often their properties do fit what is needed for a Manual Trans.
There are different Trans Fluid, if its not gear lube, but trans fluid, theres a safe bet that it has friction modifiers in it. Same with LSD Fluid, as well, you can add Friction Modifier to the Gear Lube for a LSD.
But all these things need a certain formulation of Friction Modifier and some other properties of the fluid. That is why its best to just use exactly what is recommended for the trans or axle. Manual Trans seem to do well with some of the aftermarket fluid, that are NOT specifically recommended for it, because manual trans are less critical on the fluid as long as there is enough friction modifier, which a lot of the favorite aftermarket fluids have more than enough. ATF, I wouldn't use it in a manual trans unless it was recommended to use ATF, and many are. I'm sure ATF would work in many Manual Trans, but I wouldn't be surprised if they created some problems.
Some manual trans have big hunking synchros, so friction modifier isn't that critical. So there are few manual trans out their that just plan old Gear Lube or Motor Oil is recommended as the fluid. In this case, sure use what recommended, but NEVER use Motor Oil or Gear Lube is something else is recommended.
As well, Open Differentials have no friction surfaces, plain old Gear Lube is best for them.
I have no experience with Transfer Cases, but I am almost positive they do have friction surfaces in them, how else do you engage the various modes with a lever? That is most likely why ATF is recommended, and using simple Gear Lube or Motor Oil would cause problems, you need the friction modifier in the ATF.
AS well, Synthetic Fluids are superior to Conventional Oil. We can argue for days about if its worth it or NOT, or if they really create an impovement or NOT, but most agree there at least a few cases where switching to Synthetic Fluid is like night and day in peformance, that is a few cases, NOT all. RichP seems to indicate that this is the case with the Transfer Case.
