Zener diodes are constructed in a way so that in reverse-bias the zener effect causes current to flow. This can be controlled (at time of manufacture) to a certain voltage. In forward bias the operation is identical.
Wikipedia page on Zener effect (tunneling)
Signal diodes also break down in reverse bias but that is due to avalanche breakdown which may appear similar but is caused by something completely different. It is also generally at a higher voltage.
Do you have a part number for that 500 watt Zener? ;)
Izt (current, Zener, test) isn't the maximum current the Zener can handle, it's the current through the Zener at which the Zener voltage drop limits are guaranteed.
Like Vf versus If for an LED, except that in the case of an LED the drop is generated by forward current through the LED, while in a Zener it's the diode's reverse current that does it.
The maximum current a normally reverse-biased Zener can handle is dictated by its power dissipation rating, and that power will be the product of the reverse current through the Zener times the voltage dropped across it at that current.
For example, since P = IE, a 6.2 volt Zener rated to dissipate 1 watt maximum continuous can sustain a Zener current of:
Iz(max) = P/Vz = 1 watt/6.2 volts = 161 milliamperes
Notice that if Izt is 20mA, that's well within the diode's rating.
On the other hand, Iz(max) for a 12 volt, 1 watt Zener would be about 83 milliamperes, so a 20mA Izt would still be OK.
As the Zener voltage increases, however, an Izt of 20mA will cause the one watt spec to be violated at Vz >= 50V, so Izt must be lowered, as gbulmer noticed, for the higher voltage diodes.
For example, a 100 volt 1 watt Zener with an Izt of 20mA would dissipate 2 watts, so its Izt must be lowered to 10mA just to meet the spec, and lower than that if the current into the load the Zener is working with decreases, which will offload that current into the Zener since it's a shunt regulator.
Incidentally, here's a link to an excellent, relevant resource.
Best Answer
From your comments I see that you have to make a distinction between the forward voltage of a PN junction (diode) and the reverse breakdown voltage.
The forward voltage is dependent on the material. Example: a silicon diode has a forward voltage of around 0.7 V while a Schottky diode (which uses a metal-silicon junction) has a lower forward voltage of around 0.2 V.
The reverse voltage relates more directly to zener diodes. Remember that a zener diode is used "in reverse". If you don't use a zener diode in reverse, it will have a forward voltage similar to that of a "normal" silicon diode: about 0.7 V.
The doping levels of the P-type and N-type silicon do influence the maximum reverse voltage that a diode can withstand before it shows breakdown (starts to conduct).
This is because the thickness of the depletion regions is directly related to doping levels. Low doping levels result in a thick depletion regions and a higher breakdown voltage.