Another way to think of this single/two/three-phase discussion is to know that you are not seeing two phases of a 3-phase supply grid at your home's meter base. The electric utility will run two, 120V lines and a center-tapped neutral that are feed from a single phase of a three-phase power supply from the utility (utility substations are usually fed 13.8kV or 4160V, depending on the distance from the source). A transformer will step down the voltage to 240 (generally) on a single phase and the N splits it (center tap) so you get two lines of 120V to the meter. If your meter were to be fed 120V from two of the 3 phases, then you would only get 208V between the two phases.
