BMW Differential Tutorial, with pics.
So I thought I should educate the BMW masses with my knowledge of BMW differentials. Here goes.

Earlier BMW models were nice in the fact that gear-sets and LSD units were interchangeable. Any BMW running the Type 188 (small case) gear-sets in the diff are swappable. Same thing goes for the Type 210 (large case) gear-sets.

Type 188 cars:
All E36 models, except the 3.2lt M3.
All E30 6cyl models.
All E34 models, except the M5 and 540i.
All E32 6cyl models.

Type 210 cars:
E46 M3 and E36 4door M3.
E34 M5 and 540i.
E32 740i and 750i.
All E38 models.
E39 V8 models, could be all models but not sure.

Here are pics of 2 E34/E32 diffs, 1 E34 and 2 E36 diffs. The two large case (type 210) E32/E34 limited-slip diffs on the left. A small case (type 188) E34 diff in the centre. Two 3.15:1 limited-slip E36 diffs on the right.
Here is an exploded view of the internals of a type 188 open diff.
From left to right: Two output shafts, Open center-portion, Ring gear, Speed trigger wheel, Pinion gear, Input flange, nut.
Here is the type 188 E34 case, below it is the type 210 E32/E34 case. Note, small case has 6 bolts, big case has 8 bolts.
Type 210 output shaft, 36mm dia. Type 188 output shaft, 30mm dia.
With the output shaft removed you can see the limited-slip center-portion, it has the allen key hexagonal shaft.
Open center-portions have a round shaft.
All BMW diffs have tags saying if its limited-slip (S) and the ratio.
Here is the oil I use for Limited-slip diffs.
BMW changed the differential design on the later models with type 188 gear sets like the E46, these won't work with the type 188 Limited-slip center-portions.

from here