For what you are asking, there are three types--Locked, limited slip, and open.
An open axle is torque controlled. Which ever axle has the most torque, loses the power. It's like socialism--the squeaky wheel gets no grease.
Limted slip (posi, Gov-Lock etc) is the same as an open axle--it has all the same gears that make an open axle brilliant, but suck. The difference is that there are clutches that are supposed to pinch together under load and force the diff to send power to the tire that has traction available. It's better than nothing, but still bad.
An automatic locker like a Detroit No-Spin or a LockRight or an Aussie, is speed controlled. When it goes around a corner, the outside tire is driven by the road and is going faster than the inside tire. This causes the outside tire to unlock. If you want it to herk and jerk, acclerate hard enough to bust the inside tire loose and you can have a nasty axle.
You have to drive it easy, but you can forget about a Lockright after a while. The No-Spin in my bigger truck is constantly making horrible noises, even though I know the axle is set up perfectly.
One bad thing about a locking axle--where I live, I'm often facing a steep turn onto a road with a 10,000# trailer and a heavy grade. You have to remember that with a Detroit Locker, you can't just floor the pedal. You have to nurse the trailer out flat, and then feed in the throttle so you don't risk breaking an axle. Only one axle is carrying the thrust in turns.