Predictive control is attracting more and more attention in the area of power converters and motor drives. Among various predictive control methods, finite control set model predictive control (FCSMPC) and direct current control (DCC) are two well-known approaches. FCSMPC is a powerful control method, because it takes the precise mathematical model into consideration and is easy to consider various constraints. However, FCSMPC requires large computation when calculating the cost function for each discrete switching state. DCC can solve this problem effectively. Only one prediction is required to select the best voltage vector in DCC. Despite the extensive publications regarding FCSMPC and DCC, no attempt has been made to reveal the inherent relationship between them. This paper fills this gap by investigating the advantages and limitations of each method, and what's more, pointing out their equivalence in some cases. The theoretical analysis is confirmed by both simulation and experimental results from a two-level voltage source AC/DC voltage source converter (VSC).