IMHO, whether you call 240V or even 208V single phase or two/dual phase really should come down to whether the neutral is part of the load's circuit or not.
Three phase grid/commercial is "blatantly" three phase because there are three separate AC waveforms on three separate wires, 120 degrees out of "phase". We can easily view this because we can pick an independent reference point when making our voltage over time graphs. This definition hasn't changed since the 1800s.
For residential, we center-tap the secondary of the grid's step-down transformer to split 240V into two 120V outputs, each 180 degrees from each other. If we graph our voltage over time for this using neutral (& ground to some extent) as our reference point, we see the SAME sine waves as the three phase, with the ONLY difference being that there are only two phases 180 degrees from each other, instead of three phases at 120 degrees from each other.
So while it's true that for N.A. residential there is only a single grid phase feeding your house transformer, we are essentially creating another "phase" by splitting the transformer.
Older electrical codes allowed 240V outlets with NO neutral. In this case, there can be only one phase as far as the load is concerned, because it can't use ground as part of the circuit. When graphing voltage over time, there is only a single sine waveform visible.
However, if I come along and reference ground with my two test equipment probes, I will see two waveforms, one on each wire, 180 degrees from each other, AKA two phase.
Newer electrical codes add a neutral back in to the 240V outlets, so again in this case you have two phases/waveforms. There is just no getting around it.