In fulltime 4x4 power is transmitted equally to the front and rear wheels, while in part-time
You've got the correct answer, except that that from my recolection Jeep phrases the wording from a drivers point of view. Part time by their definition means you only can drive it some of the time (part time) in that position because the front and rear diffs are locked together.
Full time means you could drive the vehicle all the time (full time) if you wished, because the transfer case uses a center differential to split torque equally from front to back.
Full time is good for highway ice and snow because it drives very much like a rear wheel drive and all wheels can find their own speed on corners or if you back off the accelerator in a skid. Part time on ice is sketchy in corners and can get pretty dicey if you should get out of control on the highway.
The negative of full time is that the centre diff limits the torque to that of the wheel with the least traction, so if one wheel is off the ground, you have no torque to any of the wheels.
In my view (select trac) has been one of Jeep's best kept secrets. There is no automatic clutching etc, just good ol predictable mechanics, yet by moving the lever to part time you have the same operation as a conventional (command trac) Jeep. A good daily driver set up.
I don't know if it was always true, but when I bought new, select trac was only available with an auto tran.