first, understand why there is a differential (if you don't) and then they why
of the various things to then try to simulate a solid axle again...
If the axle is solidly connecting the two wheels for that axle...there is a large
chance the axle will break soon or over time trying to keep both tires spinning
at the same RMPs...going over the different circle radius shown in my above diagram
A differential will allow the two tires to rotate at different RPMS to save
braking the axle
But...the down side is that an 'open' differential will only spin ONE tire if
the vehicle is on slipper surface(s)
That can get you stuck in a hurry...even faster if that one spinning is allowed
to spin really FAST...it will dig a hole deeper...
LS (limited slip) differential has the two axle halves connected to a clutch or
some such mechanism to 'try' to keep both connected as if a solid axle. Again
the above diagram and the rear tires going at different radi...an LS will try
to get both at the same RPM, but will 'slip' because of the clutches (or whatever
that OEM employs to tie the axle halves together)
LS, locker, etc are just trying to keep the axle halves spining at the same
or similar RPMs to keep enough traction to keep going in slippery conditions
AWD or full time 4x4 is just that...there is a 3rd member in the transfer case
to allow the two drive shafts to spin at different RPMs (ref diagram again)_and
NOT break one of the drive shafts or their U-Joints, etc...
LS, locker, etc makes 4x4 even more effective...