So, just an induction motor employed as a generator? Yes there IS an ac magnetization on the stator winding. Spin the shaft, and a sine wave appears. An induction generator is an electromechanical sinewave oscillator. Small residual polarization of iron parts gets it started, and it builds up as a mechanically-driven RLC resonance between the capacitors and the generator inductance (but operating way off resonance, of course.)
In that case the "synchronous" speed would be the frequency of the AC signal measured at the stator coil (or at cap bank terminals,) same as when running in motor-mode. The slip is then taking place between this coil frequency versus generator rotor RPM. Just put the AC frequency in terms of RPM = 2/#poles x 60 x HzFreq
So, if a 4-pole induction motor (as a generator) with a particular capacitor value puts out 70Hz across the cap bank, the b-field inside the motor is rotating at 2/4*60*70 = 2100 RPM. If the actual shaft RPM is 2200, then slip factor is (2100 - 2200)/2200 = -0.045 I put it as negative slip, since it's opposite of the grid-driven slip of an induction motor.
I haven't messed with one of these beasts myself, so take this all with a grain of salt.
Classic diy page: QSL ham radio site
In an induction motor, the speed of the rotor structure is always less than the speed of the stator field. However the rotor field rotates faster than the rotor structure so that the rotor and stator fields are synchronized with each other.
In a synchronous motor, the rotor magnetic field is produced by permanent magnets or by DC current in the rotor winding. In either case, the rotation of the magnetic field of the rotor is mechanically fixed to the motion of the rotor. For uniform torque to be produced, the both the rotor structure and the rotor field must move synchronously with the rotor field.
In other words, both synchronous and induction motors have synchronously turning magnetic field with torque produced in proportion to the angular displacement between the stator and rotor magnetic fields. In the induction motor, the rotor structure must turn at a slower speed than the magnetic fields while in a synchronous motor, the rotor structure must move synchronously.
Re: Question Edit
In a synchronous generator, the stator magnetic field rotates behind the rotor magnetic field with respect to torque angle. It is the relative motion between the rotor magnetic field and the stator windings that allows the magnetic field of the rotor to produce current in the stator. The current produced produces a rotating magnetic field in the stator that is synchronous with the rotor magnetic field but has a torque angle displacement.
Best Answer
The synchronous speed ns of the stator field is directly related to the mains frequency and the number of (magnetic) poles in the stator and is expressed in revolutions per minute [rpm]:
$$n_s = \dfrac{120×f}{p} \text{[rpm]}$$
The rotor speed nr is is the number of revolutions per minute of the rotor.
Slip is the ratio of the speed [difference between stator and rotor] to stator field speed. Slip is defined as:
$$s=\dfrac{n_s-n_r}{n_s} $$
So if the rotor is:
Li-aung Yip explained in his comment that slip speed is probably defined by the difference in stator speed and rotor speed, in other words: "the slip percentage expressed in RPM":
$$s_{rpm}=n_s-n_r$$