Split start induction run motors
The phase relationship between current and voltage in an ideal inductor is indeed 90 degrees.  In an ideal inductor, the impedance would be all reactive, so that the impedance would not have a resistive component.  However, in the real world, coils have both a resistive and reactive (inductive) component, so that the phase shift is always less than 90 degrees.  In a split-phase motor, the coil windings are designed so that the auxiliary winding has a higher resistance-to-inductance ratio, so its current is phase-shifted a lesser amount than the main winding.