waross described it perfectly.
I've serviced blow molding machines that were sequence controlled by type of device.
They were actually quite complex, having 20 - 30 switches, having multiple other control devices integrated into the control.
Those machines drum controllers were sequenced with a solenoid and ratchet... a dead simple and rock hard reliable electro mechanical gizmo.
At each stage they cause a function to occur until its completion, whether that is based on an actuator meeting a limit switch, or pressure switch, or light sensor, or if it was a timer. When that condition was met it would index to the next step.
Super reliable. These things were a decade older than me when I worked on them, and the drum timer was not the problematic part.