The "240-0-240" with 480V is a 2 Phase X-0-X system at 180 deg Phase from each other, basically 2 in-phase 240V sources connected in series
This (and the 120-0-120/240) is not called "two phase", but "center tapped single phase".
Multilple phase (so two and more) naming is used only, when the phases are able to form rotational field, so the phase shift must be other than 180dceg.
There are two phase systems in use (as far as I know, only in the North America; as an industrial system), most of them mare based on a delta output of a 3-phase transformer, where one of the wires is grounded. So the result becomes one Neutral and two phase wires, with 60deg phase shift (if I calculate well). It still has a rotational field (for a 3-phase load connected to these wires), yet there are only two phases.
In the history was tried a 90deg phase shift system, in fact the first Tesla's concept (it is the most obvious way to mathematically describe rotating vectors: Just use two coordinates, "X" and "Y" and let each the phase voltage represent each of them).
It was only later changed to the more economical (but not that mathematically obvious) three phase system (same three wires, but with equal load sharing and lower voltage towards ground, so way cheaper or lower losses for the same construction and power level).