Ok when in 2wd the left wheel - axle and part of the front diff spins when going forward. In theory the other half of the diff spins backwards along with the intermediate shaft until the central locking collar. Now the right side wheel and the remainder of the right side axle spins forward. Also in theory the front drive shaft should remain still.
Now the front axle as well as the transfer case are filled with lube oil, so you start turning something bathed in oil the pieces near it start to move with it. They are not being driven, they move with the kinetics of everything around them moving.
So the answer to what is moving in the front axle when in 2wd, hopefully everything. It's the sign that all parts are well lubed and free moving and drag is minimal.
Now for 4wd - In the transfer case when 4x4 is engaged a slide ring locks the collar to the shaft that is the front output (drive shaft ) that is driven by the rear output at a 1 to 1 ratio. As the front drive shaft is locked in and up to speed and again in theory the front diff now has power potential everything should be spinning in the same direction the same speed. Once this is achieved the central lock ring is signaled to engage the intermediate axle to the right side axle to complete the front drive mechanicals.
Your front and rear diff are open. As power is applied the truck actually twists and the torque transfer from the drive line believe it or not places a little more weight on the cross corner tires causing the other two to spin. That either ices the surface under the tire or carries a little more water into the mud making that tire easier to turn. As for in the air the front driver is the shorter side to put power through and the rear it's physics 90% of rear drive vehicles (without lockers) will spin the passenger tire.
In 4x4 the front and rear drive shafts turn the same speed. So the front and rear axles turn the same speed. Going straight ahead this is ideal, when turning though the front will start to travel farther than the rear (remember the track circles of a vehicle from auto class) or look at your own tracks in the snow, sand, mud and notice the front circles are larger than the rears. Now remember the front axle and rear axle are trying to travel the same distance. Can't happen drive line gets tight and something has to give, hopefully it's traction. Some times it's u-joints, axles, central axle engagement ring, or a chain jump in the transfercase.
This is very rough explanation, any questions please ask.