Inertial mass is the mass defined by Newton's famous equation
Force = mass x accelerationGravitational mass is the mass defined by;
Force = mass x acceleration due to gravityEinstein proposed that inertial and gravitational mass were identical physically, even though they appear in two different equations defining forces and accelerated motion. Einstein's conjecture, which forms the basis for general relativity, has been tested with increasing precision, and the equality:
inertial mass = gravitational masshas been found to hold to 1 part in a million or so, I believe. What isn't know is whether matter and anti-matter behave the same way, only that inertial and gravitational masses based on ordinary matter seem to be identical.