Open means the easiest wheel to spin gets the power, which is why they get stuck so easy.
Posi(positraction) is what GM calls theirs, L/S(limited Slip) is what Ford calls theirs, they are pretty much the same thing, if one wheels starts to spin faster than the other the "clutch" will apply some of that spin to the other wheel, giving it some power, BUT if one wheel looses traction completely, i.e. raised off the ground, it will act almost like an Open differential, but for ice, snow, dirt and gravel it is way better than Open.
Because this type of set up is not an instant engagement to match wheel/axle spin, going around corners is not an issue.
Lockers, lock both axles to turn with the drive line, very hard to go around a corner this way, lol, but both wheels get equal power.
What will you be racing?
On road, off road
Straight line, track, ect............