David Jones made a tutorial on the fundamentals of zener diodes over his EEVblog youtube channel.
David started the tutorial comparing between zener and regular diode. Both have the same characteristics and same I-V chart, but zener is designed to work in the negative voltage region.”In theory” the regular diode can work in the negative voltage region, but the breakdown voltage, Vb the minimum reverse voltage that makes the diode conduct in reverse, is really high. For example, 1N4148 Vb=75v and this value it is not usable in practical circuits, while Vb in zeners is designed to meet our needs. So diode effectively stops current in negative region until the voltage reaches Vz where it starts to contact current.
David highlighted the difference between Avalanche breakdown and zener breakdown. When you use zener with Vr (aka Vb)<5V then you will have zener breakdown effect and above that you will have Avalanche breakdown effect.
For more detail: Zener Diodes In Theory and Practice