What's the difference between this two methods of "tap switching"? do they work the same?
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No, the circuits are not the same.
I removed the "fluff" (the rectifiers are irrelevant) and added labels.
The top circuit can output 4 different voltages if the voltages across the separate windings are all different.
The bottom circuit can only output 3 different voltages, when S2b is in the "C" position, switch S2a does nothing.