The physical link between starter and core rotor is two sets of bevel gears, one in the accessory gearbox (I'll call it AGB) and the other on the core shaft; these two are linked by a shaft called the radial driveshaft or quill shaft.
Go back to post #14 to see the AGB and quill shaft.
During starting the starter is turning the engine, along with fuel pump, oil pump, electrical generator etc. Once the starter drops out, the engine is turning those accessories.