The 240V that you're talking about is what I mentioned as 'mirroring'. There definitely is such a thing as two-phase power, my electric car charger is 208V from two industrial phases, and our reflow oven is 208V, from two similar phases.
Well, it would be the same as single-phase power (to the device) if the devices were not connected to the neutral. The oven actually takes one of the phases (along with the neutral), and uses it to power some accessories.
With the massive caveat that I don't have a first principles understanding of any of this: I don't thing any individual load in your oven takes both legs and the neutral to do work. They're all either 120v or 208v single phase.
Aside: a lot of motors can run on either 240v single phase or 208v single phase (or, presumably, anything in between?). Take a look at Grainger or McMaster-Carr.
