I know that IZT is the test current at which the zener's reverse voltage is established. But what is IZ? (So I can enter the characteristics of one in CircuitLab.
Your question refers specifically to CircuitLab. Here is the dialog in question:
It is clear here that what they call I_z is actually Izt. They call the dynamic impedance of the Zener R_S, on the datasheet it will likely be called Zzt, and it should be the value at Izt.
The datasheet will probably give you a maximum value for Zzt, which is likely much higher than the 'typical'. SPICE models usually use the typical values. In the particular case of the 1N4742, the datasheet maximum is 9 ohms, which is almost an order of magnitude higher than the typical.
By looking at the usage of I_Z in these datasheets
I assume that I_Z is the nominal zener current. Meaning the current which typically causes the rated zener voltage. Less current will cause a lower zener voltage, more current will cause a higher zener voltage.
In case of the type 1N4728A from the first datasheet you would have to set U_Z to 3.3 V and I_Z to 76 mA to model the typical characteristic within CircuitLab.