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The difference is in the voltage of the batteries. The original ones was mercury based. For some good reasons these are no longer available....
Many of the Accutrons will run well on the new (similar sized) higher voltage batteries (1.55V compared to 1.3V if I remember right), however some will run too fast. I have several movements based on the Accutron, and 3 out of 4 runs fine on modern replacement batteries.
Paul at Electric Watches have plenty of info, and he can also service and adjust the movement to run on the 1.55V modern cells.
There is really not much electronic going on in these watches. They are at heart quite mechanical. The adjustment made is to lower the amplitude of the oscillating circuit (the tuning fork) running on the higher voltage level.

For detailed info follow this link.