We should begin with a solid understanding of exactly what moment of inertia entails. When measuring MOI, the distribution of mass distanced from the centre of the objects rotation is evaluated.
Related to golf clubs, if each club in a set requires a different amount of force to swing the club (set the club in motion to rotate around our body), it stands to reason that the golfer cannot be as consistent swinging each different club in the set.
In most simple form, this is what sets MOI matching apart from matching clubs to the same swing weight.
Swing weight matching does not make each club the same in terms of the amount of force required by the golfer to swing each club and hit the shot.
MOI matching does.
However, because golfers can be quite different in there tempo swing mechanics and strength, the right MOI must be identified and fit for each golfer to allow the concept to work properly.