It has been previously demonstrated that currents in HTS non-insulation (NI) coils exhibit a discrepant distribution during charging and discharging. However, for NI closed-loop coils, novel phenomenons that arose from the current discrepancy have not been fully studied, especially during transient processes after charging and discharging, or more strictly speaking, after the persistent current switch returns to the superconducting state. For example in our project of a prototype maglev system, a rapid decrease in the magnetic field was observed immediately after charging, which could be easily misinterpreted as a sign of local damage. However, the subsequent stability of the magnetic field with the expected decay rate of < 1\%/day illustrated that there was no such damage. To address this issue, in this study, a NI closed-loop coil was fabricated and simulated by an equivalent circuit model (per 46 turns as a L-R circuit element and 20 elements in total for 920 turns) coupled with a 3D finite-element-method model. Simulated results were in reasonable agreement with experimental measurements, demonstrating a significant discrepancy in azimuthal currents during charging and discharging; this is essentially due to variations in inductances across each turn of NI coils. Besides, azimuthal currents may initially flow in the direction opposite to the coil voltage in turns with lower resistivity relative to other turns. In correspondence with the observed novel phenomenons, after charging or discharging, azimuthal currents undergo redistribution until converging to a stable value, which exhibits a transient process and leads to a rapid decrease or increase of magnetic field in specific positions. The following issues were also discussed: 1) The judgement of operational current could be disturbed by the discrepant current distribution, due to its impact on the spatial magnetic field, not only for NI closed-loop coils but also for open-loop ones; 2) The non-uniformity of currents in NI closed-loop coils is lower, compared to that in open-loop ones with the same joint resistance and turn-to-turn resistivity distribution; 3) A new strategy with multiple charging processes is necessary for precisely charging NI closed-loop coils to the target current.