Is the reverse biased breakdown of a rectifier diode a reversible process? That is, if the voltage is reverted to a value within the specification range will the diode behave as expected of an ordinary diode, or will it cease to be functional anymore? If no, then how is the difference of behavior between a rectifier diode and a Zener diode implemented?
A normal diode will will break if you go over the reverse breakdown voltage if the current is not limited.
A Zener diode is made to work in that area.
You can compare a reverse biased Zener diode with a forward biased diode but with a much higher forward voltage (like if you set a few of them in series).
There are also avalanche diodes (en.wikipedia).
These are made to survive the reverse breakdown.