The older style differential uses an outer roller bearing without an integral inner race, so that the rollers run directly on the axle shaft. The outer seal is a separate element, that seals around the axle shaft outboard of the outer bearing. Also, the axle shaft is held in place by a circlip at the inner end of the shaft, inside the differential gear set. If you had to remove a circlip after removing the cover to pull the axle, then you have an older style differential. The seals are easy to replace, but the bearings tend to destroy the axle shaft surface that they run on if the oil level gets too low.
The newer style differential uses a shielded bearing with an integral seal and integral races (both inner and outer). The bearing is held in place on the shaft by a pressed-on retainer ring. To remove a shaft, you just remove the four bolts that hold the retaining plate to the differential housing, and use a slide hammer to pull the axle out. If the bearing becomes damaged, it can just be replaced and usually the axle is fine. To replace a leaky seal, however, the entire bearing must be still replaced (the seal is part of the bearing), which requires that the retainer ring be chiseled off, and a new ring (and bearing) be pressed on to the shaft.
As I understand it, the reason that the disk conversion won't work on the older style differential is because it is a "floating" design, in that the axle is allowed to move side to side a bit. The newer axle is "fixed" in place by the outer retainer ring. Since the caliper is "fixed" (unless a floating caliper design is somehow engineered), it can only be used with the newer differential.
Here's a picture of the older differential: