Over the last decade, frequency-droop-based control schemes have become the preferred solution in microgrids dominated by power electronic converters. More recently, the concept of virtual synchronous machines (VSMs) has emerged as an effective method for adding virtual inertia to the power system through the control of power electronic converters. These two approaches have been developed in two separate contexts, but present strong similarities. In fact, they are equivalent under certain conditions, as demonstrated in this letter. Analysis of this equivalence provides additional physics-based insight into the tuning and operation of both types of controllers.