Your model transmission probably has it's own differential oil chamber. Is your transmission 3 speed? 1-2-D-N-R-P? The same year vehicle was built with two different automatic transmissions, 3 and 4 speed. As I recall, the 3-speed had it's own differential fluid chamber with it's own drain and fill plugs. No dipstick for differential oil. The dispstick you have for the transmission is for the main fluid chamber, which uses ATF. Replacing transmission fluid you see on the dipstick, does not drain or fill the differential, they do not share fluid.
I have seen the diff going bad due to low oil level, because 99% of technicians do not know it has it's own fluid.
If you drain it over a sheet of white paper, you will likely see metal shavings. I'm afraid it's time for a new (used?) transmission. Getting a used one is a gamble, because who knows if the differential was ever serviced on it either.