Do induction motor stators and rotors have star or delta winding configurations?
The stator can be either star or delta. Many motors have a winding scheme and coils with six connections that allow the windings to be connected in either star or delta. The rated voltage for the star connection is 1.731 X the rated voltage for the delta connection. That way a motor can be designed to run at either of two voltages, 240 V or 415 V for example. Also motors can be started with the star connection and then switched to the delta connection. With that scheme, 240 volts would be applied to the star connection to start the motor at 58% of rated voltage. That would reduce the starting current at the expense of limiting the starting torque. Once the motor has reached a sufficient speed, the connection is switched with contactors to the delta connection for continuous operation.

In the USA, nine-lead motors are very common, they have a set of three star-connected windings with three leads brought out to the junction box. An identical set of windings with six-leads can be connected in star and connected in parallel to the power source for 240-volt operation. A parallel neutral connection is not required. For 480-volt operation, the additional windings are connected in series with the star-connected windings.

The rotor of a squirrel-cage induction motor is a number of rotor bars connected at both ends. That is essentially a delta connection. That is mechanically the only way the rotor bars can be connected to form a closed circuit. On the other hand, a wound rotor always has a star connection because that allows the external connection of resistors in series with the windings. For either type of rotor, either a star or delta stator can be used.

Whatever other minor advantages and disadvantages there may be with star vs. delta windings, they do not influence the wide use of either winding. I believe that other differences are rarely studied.