On level equally dry surface, traction on all 4 tires is about equal.
On level equally wet surface traction on all 4 tires is equal as well.

2 components are involved in creating traction:
1.) A specific friction coefficient between two materials (rubber and dry asphalt, rubber and wet asphalt, rubber and dirt, rubber and mud, rubber and mud, etc. - that number varies from 1.0 to 0.1 - 1.0 is best) -
2.) the weight pressing the tire to the ground (more weight is better).

On level, equally conditioned surface traction on all 4 tires is equal. All 4 tires can generate generate equal amounts of torque and forward movement

On pavement and other level surfaces all 4WD systems generate equally high torque at all 4 wheels as long as the entire surface is identical. Only when the surface condition is equal under each tire, traction on all 4 wheels is equal. Only when traction is equal at each wheel equally high torque can be generated. Only then all 4 tires rotate equally and enough torque is generated to move the car. Full time 4WD, part time 4WD, 4Hi, 4Lo - doesn't matter they all do the same thing.


Up to this point its easy.
When the scenario changes, 4WD becomes a more complex issue.

When the road (still level ground) has a mixed surface, like asphalt mixed with patches of mud or ice here and there, the scene changes.
If , lets say the front right, encounters a patch of ice - the front right will have less traction and the front right tire will eventually start slipping and spinning. Here is why:
Front left has good traction (asphalt coefficient of friction = 1.0) front right has bad traction (ice coefficient of friction = 0.1). The differential is a device that reacts to differences in resistance (traction) and makes it possible to have tires rotate at different speeds. Left side has high resistance - right side has very little resistance. The differential allows the right tire to rotate faster and spin. .A slipping wheel can only generate a small amount of torque - the one with more traction will get the same amount of torque. Both amounts together might not be enough to keep the car moving.

The differential was designed to do its job in a turn. To allow an inside tire (which puts up more resistance) rotate less and allow the outside tire (which puts up less resistance) to rotate faster. It is a "stupid" box. When it encounters different resistance (traction) due to surface conditions it "thinks" it is a turn. In this case it thinks the right tire with less resistance is on the outside of a turn needing more revolutions. That'll send the right wheel spinning faster than the left. Problem is, that an open differential always distributes torque equally and the slipping wheel determines the maximum of torque to be generated.
But not all is lost. Since your rear axle generates torque as well, the rear tires are able to keep the vehicle moving. But only if you drive a part time 4WD vehicle or a full time 4WD with center diff in locked position!

If the center differential of a full time 4WD were open (unlocked) in the above described situation the vehicle would not be able to maintain uninterrupted forward motion.

Here is why:
The front right wheel is slipping and spinning because it has less traction than the front left wheel. The front axle differential allowed the right wheel to rotate faster. The center differential (the one that sits inside the transfer case) acts the same way axle differentials do: It senses and reacts to resistance. It senses less resistance at the front differential. It reacts by allowing more and more rpm to go to the front axle and proportionally less to the rear. The resistance of the front axle determines how much torque can be generated (not much). The rear axle will get an equal amount of torque. If both amounts combined are less than needed to move the car - it is stuck.

Using the center diff lock keeps the center diff from allowing independent rpm at the two driveshafts. It forces the driveshafts to rotate at equal speeeds (like a part time system would) to help maintain constant forward movement. With the center diff locked the total amount of torque generated (2 times the amount that can be generated at the point with the least resistance) is no longer determined by the axle with the least resistance - it is now determined by the axle with the most resistance. A car with center diff lock has a higher likelyhood to keep moving in mixed traction situations than one without.

To make traction management more transparent to the user and to avoid that the driver needs to make essential decisions to stop wheel spin, most manufacturers have incorporated mechanical (Torsen), mechanical/hydraulic (Gerodisc) or electronic (ETS, Haldex) traction management systems. However, they are not as capable as a manually locked center diff. That is why the best 4x4 on the market today, offer a combination of automatic as well as driver activated traction management (Mercedes G500, Mitsubishi etc.)