During the dynamic process of a system, the current control of a converter realizes a balance between current and reference by adjusting the output voltage when the grid-side current changes, which is represented as voltage response under the current excitation. Since the AC voltage of the converter is generated by controlling the amplitude/frequency and the amplitude/frequency of voltage is required to be maintained during the system operation, the current control should be described as the internal voltage amplitude/frequency response under active/reactive current excitation when a power imbalance occurs. At the same time, from the perspective of a grid-connected converter's influence on the grid, the active/reactive current response under the terminal voltage amplitude/frequency excitation is another perspective for understanding the characteristics of the grid-connected converter. Therefore, for the current control of the converter, the active/reactive current-internal voltage characteristics used in the dynamic analysis of large systems and the terminal voltage-active/reactive current characteristics from the perspective of the influence of equipment (e.g., single machine) on the grid are presented. On this basis, it is determined that the two kinds of characteristics are essentially equivalent by explaining the redundant relationship between current and terminal voltage under the current control. Finally, the equivalence is verified by simulations, and the influence of phase-locked control parameters on current control characteristics is preliminarily explored.