It is essential for a relay energized by alternating current to have

A key difference in an AC relay is the presence of a "shading coil". The purpose of this coil is to keep the relay on when the current drops to zero during phase change (note that in AC power the current and voltage are alternating in a sine wave around 50/60 times per second). The shading coil retains some magnetic energy and essentially holds the relay ON when the current drops to zero momentarily due to the AC waveform.