regarding which part uses which oil, the manual specifies:
1-engine: only synthetic engine oils approved to MB 229.3 or MB 229.5, such as Mobil 1 SAE 0W-40. should say: engine oil SAEJ300 0W40
2-automatic transmission: only use ATF approved to MB 236.10, MB 236.12 synthetic dextro III transmission fluid
3-manual transmission fluid: only use fluid approved to MB 236.2. SAE 5W-20 engine oil, meeting API SL or GF-3. should say: engine oil SAEJ300 5W20
4-rear axle fluid: only synthetic SAE 75W85 axle lubricant that meets MB 231.1 should say: rear axle oil SAEJ306 75W85
so:
1- engine uses engine oil (of course);
3-manual transmission also uses engine oil of a little different viscosity.
4-rear axle uses gear box oil. it is another kind of oil. it is NOT engine oil (the specification is SAE 75W85). the manual does not specify if this is the same kind of oil or not as the engine. in reality, it is different kind of oil
the problem is that, as mentioned before, SAE is not just SAE. there are 2 different classes.
engine and transmission use SAE J300, and rear axle uses SAE J306, and this should be mentioned in all cases, because the numbers are so far apart, that trying to use the wrong specification means havoc to the part. (it is all clear on the chart provided by pizzaguy-see post 47)
(2-with automatic transmission, the lubricant is transmission oil specific for it).
in conclusion:
1- engine and transmission use engine oil (although of different viscosity-but not much)
2-rear axle does not use engine oil; uses a different kind of oil, designed specifically for gears.
3-automatic transmission uses another kind of oil for transmission, that is specific for it.