The 2WD AW4 has a longer tailshaft, different size and spline count, and you'd have to do a "divorced" mount for the transfer case as a result.
The 4WD version has the transfer case adapter, a shorter tailshaft with a different size and spline count, and an integral "adapter" housing to bolt the transfer case directly to the transmission.
You can convert from one to the other, but it requires the mainshaft/tailshaft assembly and tailshaft housing/transfer case adapter housing, and you're damn near doing an overhaul to replace the mainshaft/tailshaft assembly anyhow.
As for the "part time" and "full time" difference - that's nothing to do with the transmission. That indicates a difference in the transfer case - the "part time" only transfer case locks the front and rear outputs together in four-wheel-drive, while the "full-time" transfer case option has a differential. The differential is "locked out" in part-time 4WD operation, but comes into play in "full-time" 4WD, allowing the front and rear driveshafts to turn at different speeds.
The use of PT4WD on dry pavement is not recommended, and eventually will result in damage to your transfer case (and probably sooner, rather than later.) The use of FT4WD on dry pavement is generally not recommended, but should not cause any trouble. It's not all-wheel-drive, but it's close. If you're expecting foul weather and have "full-time" 4WD, you can go ahead and shift into it before the weather hits to get ready. Don't want to do that with "part-time" 4WD, tho...
A vehicle with "part-time" 4WD only can easily be converted to have "full-time" 4WD available - just swap the transfer case, and change the shiftgate and bezel. Driveshafts and transfer case mounts are typically the same (at least, they are for the NP231 PT4WD and NP242 PT/FT4WD transfer cases, which are common on Jeeps.)