I'm taking my information from two sources, this Digital Trends article and the good old Engineering Explained video.
Digital Trends explains it as:
How this differs from a standard differential is that, where as a basic mechanical diff spins the outer wheel faster than the inner wheel (it has longer to travel), the TVD in the RC F employs electronic motors and actuators that apply pressure to multi-plate clutches that can control the distribution of torque.
Essentially, while good ol’ physics will get the differential to split the torque between the wheels, the electronics can now influence things when it sees fit, “vectoring” the torque where it senses the car needs it the most.
In a track application, putting a ton of torque on the inside wheel of a turn would basically put the brakes on it, having the outside of the car sort of pivot around it, making tight corners easier to handle. Specifically for the RC F, there’s three modes that can be manually selected: Standard, Slalom, and Track. Standard (surprise) is the basic driving configuration, while slalom optimizes the response for quick left-right alternating experienced on twisty back roads. Track mode puts an emphasis on keeping the rear axle stable at high speeds.
Basically, the way the differential works is it's an open differential. On either side of the differential, there are clutch packs which are motor actuated. These clutch packs lock up a planetary gear set. As the planetary is engaged, they lock the axle to the differential allowing the torque to flow out that side.
Here is what the clutch pack looks like with the planetary:
Here is a different model/manufacturer in a cutaway view, but the same basic premise:
As far as functionality, I see no real difference between using this setup, or using the ABS system to stop a wheel from turning as much to provide torque to the other side of the vehicle. It is the same basic principle, just in reverse.