A.k.a 'fast and loose' pulleys, fast as in fixed rather than quick.
As Simon says there were a number of different arrangements for starting a motor manually. Resistance starters, such as a rotor resistance for an AC motor or armature resistance for DC, would often have more than two intermediate steps, so it seems more likely to have been an autotransformer starter and you were changing voltage taps. But there were certainly some resistance starters with just a couple of steps so anything is possible.
Another possibility is that it was a synchronous motor, which was a popular choice for larger drives to keep the power factor up (and even compensate for low power factor elsewhere, by running it over-excited). In that case, the steps might have been off, star, delta, synch, but something that sophisticated would probably have merited an ammeter.
I wish I could get one of these installations complete to rig up in the museum workshop. It's a way off. I have a nice big DC motor with 8" belt pulley, something like 50hp at 110V although the plate is missing. I think it served in a wood shop, it was packed with sawdust to the point that the armature appeared to be wound with MDF. Unfortunately no suitable starter for it, although I might be getting a couple of cast iron starting pillars - the kind with drum controllers with handles on the side, and glass windows - so if we are very lucky one might have suitable resistances and coil voltages. It would run nicely off one of the mercury arcs or DC gensets.