But wouldn't multiple-phase wiring use entirely different colours? And would that be 3-phase, or some weird "2 phases, both referenced to neutral" stuff...?

Residential - 120/240v, 1phase, 3wire. Tyically Black (hot), White (neutral) and bare ground. Red wire is usually either a traveler in the case of a three way or a second hot on a different phase.

New commercial wiring is typically 120/208volt, 3phase 4wire black, red, blue, white and green (ground) or 277/480volt 3phase, 4wire which is usually brown, orange, yellow, grey (neutral) and green.