AWD System one (true all wheel drive - or full time symmetric AWD) has a conventional differential inside the transfer case - each of the wheels gets about 25% of the torque as long as traction is equal. However, the center diff cannot be mechanically locked.
To prevent a complete loss of traction when one wheel or one axle would spin, a viscous coupling or a similar device like a Haldex coupling (see note) will try to "glue" both driveshafts together to keep enough torque flowing to the axle with traction. Works kinda OK on slippery pavement when the vehicle has already sufficient momentum and the connecting device has to kick in very infrequently. Off-road or in other situations with slow speed and high demand for torque the glue box (viscous coupling or Haldex etc.) is overstressed and fails to deliver the needed torque. High torque transfers and continous use make especially viscous couplings fail. Haldex units are much more reliable but cannot satisfy the constant high demand for torque at all wheels either.
AWD System two (automatic asymmetric AWD - and in a way actually only a sophisticated 2WD system) might not have a differential in the transfer case (Volvo, Honda, etc.) but some do (Jeep Grand Cherokee). Primary power goes only to one axle (makes spinning tires much more likely due to inefficient use of traction - as likely as in any other 2WD car). However, both drive shafts are joined by a viscous coupling or a similar device (see note) and as long as all 4 wheels turn at the same speeds the control unit remains inactive. Once the powered axle or one of the powered tires loses traction, the powered drive shaft rotates faster than the one that is just rotating along. The control unit reacts to the speed difference and kinda glues both drive shafts together. This way the previously unpowered shaft will get some of the torque and rescue the failing tires. Same story as in system one: Works kinda OK on slippery pavement when the vehicle has already sufficient momentum and the control unit has to kick in very infrequently. Fails miserably when need of high torque arises or when activated frequently. Cannot satisfy the constant high demand for torque at all wheels when off-road.