Generally, high-temperature superconducting rotating machines (HTSRMs) are considered synchronous machines. If the output of the HTSRM fluctuates based on frequent changes in the electrical or mechanical loads, there is the concern that an asynchronous rotating magnetic field (RMF) is applied from the stationary copper armature winding to the high-temperature superconducting (HTS) field winding in the rotary. This may act as a magnetic disturbance to the HTS field magnet, resulting in permanent damage. To enhance the reliability of HTS magnets in wind power and electric propulsion applications, winding methods with current bypass/distribution characteristics, such as no-insulation (NI) and metal-insulation (MI), have attracted scholarly attention because of their high thermal and electrical stabilities, resulting in their self-stabilizing and protective performances. To verify the feasibility of the NI and MI winding techniques for wind power generators, the basic characteristics under a time-varying magnetic field must be studied, contrary to HTS magnet applications under a time-static magnetic field. Therefore, the electromagnetic characteristics of rare-earth barium copper oxide (REBCO) magnets applied with NI and MI winding technologies were compared and analyzed in this study, considering the magnetically transient situations in which an asynchronous RMF is applied to REBCO magnets. In addition, we developed a characteristic evaluation device similar to a synchronous rotating machine to generate the unsynchronized RMF. Moreover, various basic tests were performed to target the small racetrack-type field windings. The critical current, n-value, terminal voltage, and center magnetic field are investigated under various values of the frequency and current amplitude of the three-phase armature winding, and their behaviors are discussed in detail based on the characteristic resistances of the two test magnets.