I have had the 3D Adaptor for the Master System for a while now along with a pair of 3rd party glasses. Testing out the 3D using the 3rd party glasses never seemed to work quite right so I decided to get a pair of the official 3D glasses. Looking on eBay the cheapest glasses I found (including shipping) came with the 3D adaptor for the Mark III. Having a look into whether or not the glasses would be compatible or not with the Master System I didn't find much about the Mark III's 3D abilities any where. So I decided to chance it anyway.
After a few weeks they arrived from Japan I tested out the glasses and they were an improvement over the 3rd party pair I had. Not perfect but they seemed to work better in some games.
Comparing the two adaptors to each other, they are similar in size but the Mark III adaptor does not fit in the Master System due to the casing of the adaptor being a different shape. The edge connector looks like it would fit in the Master System so I opened up the case to compare the insides. Internally they are very similar. The Mark III board has the model number 837-6359 while the Master System board has the model number 837-6270. The only differences that I can see is that the Master System board has two pads labelled M4 and M3 with the M4 pad bridged. The M4 is referencing Mark IV (aka Master System) and M3 referencing the Mark III, one can assume if you swapped the bridging of the pads it would work in the Mark III. A couple of chips also have different part numbers.