The problem of differential protection mis-operation caused by magnetizing inrush current of converter transformers in UHVDC systems has yet to be fully resolved. This paper presents a detailed analysis of the adaptability of traditional differential protection under transformer inrush current conditions and proposes a novel method for discriminating the fault current and magnetizing inrush current based on the circular coordinate representation images. First, a simulation model for transformer internal fault and magnetizing inrush system is built in Simulink, generating a large dataset of three-phase differential current simulations. Then, the circular coordinate transformation is introduced, in which both the original and translated three-phase differential currents are treated as 2D coordinates of dynamic points. Significant trajectory differences between the two differential current under various conditions are observed, and the simulation data are further transformed into the trajectory image sample set. Finally, the classification performances of six common machine learning algorithms on the trajectory image dataset are compared. The VGG16 model, selected for its superior overall performance, is used to identify and classify the current trajectory images derived from simulations, experiments, and field recording, effectively distinguishing between faults and inrush currents. The results show that the proposed method has high prediction accuracy and avoids mis-operation in traditional differential protection. Additionally, it demonstrates good adaptability under various operating conditions and reduces the complexity of protection schemes.