Welcome to the forum.

4low is a high ratio so top speed would be about 30MPH, in Overdrive, lol, no mistaking 4low, you barely move when you step on the gas

2WD and 4High are the same ratio, but when front drive line is engaged you will feel the front wheels "pulling" when you turn, almost a wobble if on dry pavement.
4WD is not subtle, you will always feel it in the steering wheel when front axle is pulling you.
AWD cars are different, only a small % of power goes to front wheels.
In 4WD front wheels get full power same as rear wheels

Any gravel or dirt road is fine to test 4WD, you want a low traction surface.

2001 was first full year Rangers had Live Axle in the front, front wheels are always Locked, no unlocking hubs.
So one less problem.
2WD or 4WD was only based on transfer case shifting.

Electric 4WD has a switch on the dash and 2 lights to confirm 4high and 4low engagement, no lights on = 2WD
These lights will flash if you select 4WD and transfer case doesn't change.
Both of these lights should come on when key is turned on, that is a BULB TEST, not a 4WD test, just to let driver know the bulbs are OK, all the dash lights should do this with key on.

If you don't see 4WD light come on when you select it then there is a problem, if lights don't flash then probably a bad 4x4 module, which was not uncommon in early 2000's, or could just be a bad fuse.

2001 was also the first year Rangers got the 4.0l SOHC V6 engines, they had timing chain issues until 2004 model year, so heads up on that, have to pull out the engine to fix this problem.
3.0l OHV Vulcan V6 engines did not have any specific issues in 2001.