MP,
A zener regulator is always conducting current while regulating, regardless of the amount of load current. The zener conducts its wasted current to ground, not to the load. The resistor feeding the zener must supply both the zener's and the load's currents.
A series voltage regulator IC conducts only load current, without wasting any current to ground (except for its tiny operating current). So the IC will heat much less than the zener plus the resistor, above, and therefore the IC will have much less power loss.