Why is it that the right side gets worn more with an open diff? This is the first time I’ve heard of that, but it seems to have been true in my case.
It's the side that's typically receiving power in an open diff in a RWD vehicle, as
@thastinger noted. This is because it is on the ring gear side of the carrier. Similarly, with 4WD, the left front is the same way, being on the ring gear side and tending to be the wheel that gets power. Of course if that wheel has more traction, the power will shift to the other side, as an open diff always wants to send power to the wheel with the least amount of traction.
This is where the old "posi test" (limited slip test) would come into play.
Take a hold of the driveshaft with the car in the air and rotate in the direction it turns when the vehicle is going forward. The right-rear tire, with an open diff, will go forward, the left rear will spin the opposite direction. Grab a hold of the right rear tire, rotate it CW (forward), the left rear will go in reverse (CW on that side). Go to the left side, rotate the tire CCW (forward), the right-rear will now go in reverse (CCW on its side). This is why, in situation with mostly equal traction, the natural bias is for power to be sent through the right rear; the carrier side wheel, as that's the side with the spider gear that wants to go the same direction as the ring rear.
With limited-slip (of the clutched variety) there are stacks of friction disks on either side of the carrier behind the spider gears with a spring pushing the spider gears into them. In this situation, turning the driveshaft forward will result in both wheels spinning the same direction because the spider gears are "locked' together by the clutches; they are not free to spin. Grab a hold of either of the wheels and spin them "forward", the other wheel goes the same direction. With this setup, it takes force to break the friction bond between left and right, which is why a "tight" limited slip can chatter going around corners as the clutches slip. Friction modifier is added to reduce the friction, making the slipping easier and eliminating chatter. Contrarily, drag racers with cars that are still street driven will add another friction and/or a heavier spring to make it require significantly more force to slip. This is also why a truck with a limited slip is so eager to step out if the road is crowned, as both wheels naturally want to go to the same speed all the time and if neither have traction, it will slide the direction the crown wants to take it.
An automatic locker is similar, except that typically the unit functions as an open diff most of the time until traction is lost and then both shafts are locked together. An electronic locker is typically open as well, but requires power (usually a magnet or electric motor arrangement) to lock the wheels together. My SRT has a complex electronic locking rear differential that's also limited slip, so not only does it naturally want both wheels to go forward, if there is a torque imbalance that overwhelms the clutches, the unit will, electronically, mechanically couple the shafts together for maximum traction.
It likely operates similar to this Porsche unit:
Another type is the Torsen torque vectoring arrangement, which works opposite an open differential, sending power to the wheel with the most traction. These tend to avoid the "stepping out" effect you get with limited slip and lockers.