A transfercase doesn't engage any of the wheels, it engages the driveshafts. The axles determine which wheel turns when force is applied to the pinion.
2WD has the rear driveshaft engaged, and the front driveshaft is disconnected from the powertrain. The axle will decide which of the wheels gets power--if open diff then power transfers between the two wheels according to whichever wheel is spinning faster, if locked then both wheels get power, if LSD then one wheel gets power until it spins too fast and then both wheels get power.
Full-Time 4WD is essentially the same as an open diff on an axle, in that power is transferred between the front or rear driveshaft according to whichever one is spinning faster. The 242 has a slight bias to the rear axle (about 5% as I recall) so that driving straight the rear axle gets power. When you go around a turn though, the outside front wheel travels a larger arc than the inside rear wheel, so it spins fastest--as a result the axle spins that shaft faster, and the transfercase moves power to the front driveshaft. In FT 4WD you only ever have one wheel under power (again, assuming open diffs on the axle). The more common term for this mode is all-wheel drive, but the technically accurate term is any wheel drive.
Part-Time 4WD locks the driveshafts together. The front and rear axles must spin at the same rate. If you go around a turn, the faster wheel on the outside front will want to spin faster than the inside rear wheel, so something somewhere has to give.
Part-Time is really only good for loose conditions, ie gravel and dirt. It is not good for slippery conditions, since you are constantly breaking surface and might not get it back. If you get stuck in 2WD or AWD (spinning) then yeah put it in PT4WD and drag yourself out, otherwise use one of the other modes.
