Most traditional floor lamps in the US are wired for "three-way" bulbs, with two internal filaments. For example, a 100 W and a 50 W filament, to allow 50, 100, and 150 W settings.
The "four-way" switch has been standard nomenclature in the US (for a DPDT switch wired as a reversing switch) for my entire lifetime, and I'm old.
A rotary switch that has four positions is the "4T" (four throw) in SP4T (for example).