The first of the 9" differentials were available from 1957-1959 or so. These were actually 8-3/4" diffs. Something was modified in 1960 and all the production ratios seem to have changed. The result was the 9" gearset. Not sure why ford did this, but the 9" is referred to in factory literature as the 8-3/4 or 9", particularly when buying gears.
A few years later, the 9-3/8" differential was released, and it contained a gearset with either a 9-3/8" ring gear or else a gearset with a 9-3/4" ring gear. You will sometimes hear the 9-3/8" diff called the 9-3/4", particularly when buying gears. The cases seem to be the same between the 9-3/8" and 9-3/4", but I may be wrong.