none. they both have gears, and they both have high pressure additives. main thing is to check the manual for the specific application. even some cases the manual calls for motor oil in a MTF. the question should be:
what kind of oil do I use in -fill in blanks- ?
for instance one person on internet was using mobil 1 extended in the gertrag manual transmission, and it worked well, but people here were warning against it. some places mix 50:50 gear oil, motor oil for MTF and that also can work in the right setting.
The hypoid gearset in a differential takes an extreme pressure lube GL5, as it is probably the most stressed component on a car as far as pressure applied per square inch of contact surface. Transmissions get by with out the high levels of extreme pressure additives. Think about why some gearboxes live long lives using ATF.
Essentially, the difference between MTFs (or synchromesh gear oils) and "traditional" (hypoid) gear oils is the additive package: friction modifiers and EP/AW additives.
MTFs tend to be thinner and range from cST 7.0 - 15.0 where most traditional gear oils start at cSt 15.0 (90 weight) and go up from there.