The key concept you're missing is Power Factor[0]. With reactive (inductive or capacitive) loads, the current and voltage will be out of phase with one another,

The key concept you're missing is Power Factor[0]. With reactive (inductive or capacitive) loads, the current and voltage will be out of phase with one another, leading the peak current to occur at a time other than the peak voltage. This reduces the power delivered to the load to less than |V|*|A|; in a situation where you hold power demand and voltage steady, you would need to deliver more peak current. For the two power measurements, one is instantaneous power, the other is average power. Different situations call for different measurements. [0]https://en.wikipedia.org/wiki/Power_factor https://en.wikipedia.org/wiki/Power_factor