It is a bit difficult to picture without actually seeing it in operation.
Take the gear case cover off if you can, turn it and play with it.
As soon as you see it in operation, it'll all make sense...(or maybe go to an auto mechanic shop and see if they've got one to show you or something)
EDIT: I just took another look at the pictures in post #1. An open diff is exactly what it looks like to me. The motor input is slightly offset from center, the round bump on the one side is for the large bevel/ring gear, probably driven off a center mounted reduction gear setup, the spiders and side gear are probably mounted in the middle.
You never did mention exactly what this motor was from. I could be a wheelchair setup as long as it has a sort separate steering motor, unless the brakes actually accomplish the steering.





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