You can look at it either way. "Phase" literally means the offset of the waveforms. With 3-phase, each of the phases is 120° out of sync. With split phase, you can look at it as a single, 240V phase with neutral in the middle, allowing it to be split into two 120V halves. Or you could look at it as two 120V phases, 180° out of sync, such that the difference between them is therefore 240V.