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This study presents an analysis of the fatigue damage experienced by mooring systems under extreme and operational wave conditions, with a discussion on the Reference Model 3 (RM3), a widely recognized point absorber wave energy converter (WEC), and the Reference Model 5 (RM5), a floating oscillating surge wave energy converter (FOSWEC). Utilizing the combined strengths of WEC-Sim and MoorDyn, both open-source simulation tools, the study investigates the dynamic behavior of mooring lines over the operational wave condition and a 100-year return period extreme wave condition. This study highlights the relationship between tension force and fatigue damage in mooring lines. The tension forces at various nodes of the mooring lines are calculated, revealing that the complex mooring design is causing a complex trend on the fatigue damage. Instead, variations in tension force show a more significant impact on cumulative fatigue damage, as evidenced by the higher damage observed in nodes experiencing greater tension variation. The findings contribute to a better understanding of the factors influencing fatigue damage in mooring lines of WECs and fatigue damage of different types of WECs, offering insights for more effective monitoring and strategies for WEC design optimization.