Any BL motor will run on 1S with the HW 1S 120A speedo. When running lower voltage on these motors (1S at 3.7v nominal) there can be an advantage in having a smaller diameter rotor. Many companies therefore offer that smaller rotor already fitted and call it a "1S motor." You don't need a 1S motor to run 1S, not do you necessarily need a smaller rotor to get the best out of the motor when running 1S.
If you have bought the motor, you can buy the rotor separately and switch them over. The rotor is cheaper than buying a new motor. My advice is to run the motor as it is - I do and it is just fine for speed and driveability. HTH