well, automatics are black boxes of evil in my mental word, so i don't know them as well as i do manuals, but i will try to explain it, though someone else can probably do a better job.
the auto tranny uses an electronic center diff (ECD). this means that there are several sensors that the ECM uses to determine wheel slipage (not sure, but stuff like ABS wheel speed sensors, TPS, etc). as long as everything is copesthetic, the ECM keeps the ECD sending most of the toque (90%) forward with the remaining 10% driving the rear wheels. now, when the wheel speed starts to vary front to rear, the ECM will change the toque split (to a max of 50/50 IIRC), which will allow the wheels that have more grip to get more power, saving your ass from that nasty deer that jumped out in the road in the middle of a blizzard. since its electronic, it all happens at the speed of light (basically).
now, the manual system is all mechanical. the center diff is a viscous coupling LSD. this means that if a certain ring gear inside the diff starts to speed up (caused by slipping wheels) there is a fluid inside that will be heated up by the extra energy. this heat causes the fluid to become more thick, which acts sort of like a brake on the spinning axle, which means that the engine torque is going to take the path of least resistance, which is now no longer the slipping wheels, but the ones with grip thanks to the viscous fluid. but, as you can imagine, it takes some slip to exist before the torque gets transfered, so its not as quick as the ECD, although modern viscous LSDs are set up with a bit of lock in them, so that they activate more quickly. anyway, you can set what the default torque split is (in my case 50/50), and then as one axle starts to speed up (slip) more torque is transfered to the other. the amount of torque transfer is proportional to the amount of slip, until you reach the physical ability of the diff gears or fluid.
and then there's the STi's, which use a mechanical LSD in the center. its basically the same set up as a manual RS, except that the torque split is varied through a series of gears pushing against one another instead of fluid getting thick. this way is kick ass, and as a bonus, some diffs allow the driver to toggle the static torque split by realigning the diff gears (i think), which is why you can make the 22b completely RWD (as in all the torque goes to the rear wheel).
mitsubishi, on the other hand, uses electronic diffs in the EVO, in a similar engineering concept to your car, but with more intense hardware and a set up designed for Group N rally competion, not keeping people out of trouble on a snowy road
and then there are the WRC cars, which i won't even pretend to understand the level of technology there, but it is all electronic, though bears about as much resemblence to an automatic RS's drivetrain as a Cheetah does to a Pepsi. one cool thing it can do is disengage the rear drivetrain when the handbrake is pulled. Uber cool to say the least.
anyway, i hope this answered your question somewhat.