Inertial mass is the mass in the famous equation
Using the inertial mass
Consider a setup with two springs attached to either wall and a mass in the middle of the room attached to each. If the mass is free to slide across a frictionless floor, the frequency at which it slides will be determined by the mass and the spring constants. Increase the mass and the motion slows. The same forces act, but the accelerations at various positions between the walls changes in direct proportion to the mass. This setup is called an Inertial Balance.
Remarkably, inertial mass the same thing as gravitational mass. Gravity exerts a force in direct proportion to the inertial mass. If I take a 1 kilogram mass and set it on a bathroom scale, it will exert 9.8 Newtons of force on the scale.
If I do this on the moon, the gravitational force is different. The Inertial Balance, however, will function exactly the same.