Just found someones description of operation which might help :-
Capacitor-start motors use a capacitor in series with a winding and a centrifugal switch. At start-up, the cap is in the circuit to produce a phase shift, relative to the main winding, in the start-up winding. When the motor reaches some speed, the centrifugal switch will open, disconnecting the start-up winding. The overall effect is high torque at start-up, so the motor starts the load quickly. The current during startup will typically be several times the running current. The switch is a reliability concern, causing grief if it either fails to close or fails to open.
Permanent Split Capacitor motors have two windings, one directly across the line and one that always operates with a capacitor in series. Again, the capacitor produces a phase shift so that there is a "rotating" magnetic field to make things spin. PSC motors don't have great startup torque, but a blower isn't a difficult load to start and it doesn't matter if it takes a few seconds to come up to speed. The startup current isn't much higher than the running current. Reliability is improved because the mechanical switch is not needed. For a motor that starts up frequently, like a furnace blower, this is a big plus.
Capacitors are used for phase shifting for motors to run on single phase AC power. If three phase power is available (very rare for residential in North America), a motor that doesn't require caps can be used.