What is the difference between constant current and constant impedance ratings on Variac variable transformers.

Constant Current Rating:  This is the maximum continuous amperage rating at any output voltage. 

Constant Impedance Rating:  This is the maximum continuous amperage resistive load  at 100% voltage output that the transformer is rated.   The transformer has to be wired for 0 to Input Voltage (no boost) .  This rating does not apply for non-resistive loads or if the transformer is wired for voltage boost.