A powerhead is a pump, but it just circulates water. A pump circulates water, usually as a secondary benefit to what it is primarily used for.
If the goal is to drive a protein skimmer or return water from a sump into the main tank, that would be a pump. If the goal is to circulate water inside the tank, the powerhead is a pump designed to do that.
Pump= moves water from point "A" to point "B".
Powerhead= moves water around.