Hub problems are generally clicks, except for the bang when they fail under load.
Any major clunking noise is something else.
Transfer case in the '93 is pretty simple. You said "4wd motor on the back of the transfer case" so you must have the TouchMatic (or is it called TouchDrive, can't recall) push buttons on the dash.
Push the 4x4 button. Might hear some relays clicking in the back end from the shift controller in the jack storage compartment. Within a second or two, the light next to the 4x4 button will illuminate, indicating that the TC has successfully shifted. No light until shift is completed. If the hubs are already locked, you might hear/feel a small thunk as the TC engages the front driveshaft. If there is any drama, then you probably have mismatched tire sizes.
The shift into (or out of) 4low requires that you be stopped and in neutral. A push of the Low Range button and again there will be relays clicking in the rear quarter. When shift is complete, light will illuminate.
If you don't get positive shift results, try just sitting still in the driveway with the parking brake set and the transmission in neutral. It is very common for the transfer case shift motor to "gum up" and not want to shift smoothly if it has not been used recently. We used to have a '93 that my wife drove and the 4wd had not been used for a couple of years. When she tried it in the snow, no luck. I spent an hour just patiently pushing the button, listening to the clicks and waiting for the light to come on. It would take several tries before the control would indicate a successful shift. The controller clicks for a couple of seconds and then times out. Wait for the clicks to stop before trying again. After a few cycles, it would complete a shift. It would then take several click cycles before it would disengage. I just kept exercising it and each time it took fewer cycles to make a successful shift. After maybe ten shifts, it was working smoothly.
After that session, it continued to work reliably when I tested it every few months.