Wire EDM cuts exclusively in a straight line from the top head to the bottom, which can include a taper angle. The path the heads follow can be programmed to be whatever tho. I suppose something like a ribbon tool could be made for a sinker EDM but I'm not sure how well that would work. It couldn't be wire thin, but the external profile combined with a rotary head could achieve a similar result.
There is 4-axis wire EDM, where the upper and lower guides can move separtely, this is probably what you are thinking of? Or more like 6-axis?
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