How does the high inrush relay handle the inrush current?
Inrush capacity just means that inside the relay, the components are capable of dissipating the heat caused by the very brief (1-2 cycle) inrush current without causing damage. 

That has nothing to do with the "breaking capacity" of the relay. Rating of a switching device for control of a motor is not really about the inrush, it is about stopping the flow of current when the motor has been running. When contacts separate under load there is an arc that forms, and it is extinguished when the dielectric of the air is sufficient to stop the current flow. Induction from the motor will cause the voltage to rise in the arc as it forms, which will sustain the arc for longer. The arc is then melting the contact surface areas, potentially destroying them. So the capacity of those contacts to stop that current flow and extinguish that arc without vaporizing and/or welding in the process, determines the maximum motor size it can handle. If you are switching a motor, you need a relay / contactor that has a motor rating equal to or greater than your motor power (HP or kW). If the contacts have no motor rating, they are incapable of being used in that manner.