It goes from
hot-neutral-ground for 120 volt -to-
hot-hot-ground for 240 volt
I would do what you planned with 240. Forget 120. Just parallel two 240 outlets on the one feed if the use is noncoincidental so you can leave them both plugged in and ready to work. If your alone it will be fine as no way to load both up at same time. It isn't really code but nothing unsafe about it whatsoever.