This paper qualitatively explores the relations between two kinds of side-channel leakages, i.e., the fault sensitivity (FS) and the power consumption. The FS is a relatively new active side-channel leakage, while the power consumption is one of the earliest researched passive side-channel leakage. These two side-channels are closely related with regard to both the security evaluation and the countermeasure proposal. This paper experimentally answers the following important issues such as the relationship between these two side-channels, whether they share the same leakage function and whether they can be protected by the same countermeasure. Based on two FPGA AES implementations without countermeasures, we first confirm a high correlation between the power consumption and the FS. Then, we construct the leakage profiles for the FS and the power consumption to explain the detailed relations between them. We also confirm a successful key recovery using the FS profile as the leakage model for power consumption. Based on these discoveries, we believe that FSA can be used as an evaluation tool to find the first-order leakage with less data-complexity, and it is more reasonable to achieve the countermeasures against FSA and power analysis from different design levels.