This effect doesn't change the mana cost or mana value of an artifact spell. Rather, it reduces the total cost of the spell, which is the amount you actually pay while casting it. The total cost takes into account additional or alternative costs.

This effect can reduce only the generic portion of the artifact spell's total cost.

The only difference between a colored artifact and a colorless artifact is, obviously, its color. Unlike most artifacts, a colored artifact requires colored mana to cast. Also unlike most artifacts, a colored artifact has a color in all zones. It will interact with cards that care about color. Other than that, a colored artifact behaves just like any other artifact. It will interact as normal with any card that cares about artifacts, such as Shatter or Arcbound Ravager.