Awemason has it right.

Basically there are two topologies when dealing with induction power supplies.

#1) Variable DC Buss, with the inverter running at (or very close to) the tank's natural resonant frequency. - This is the on that Awemason has described.
Basically in this mode, the power (or voltage applied to the tank) is controlled by the amount of DC Buss voltage achieved.

#2) Fixed DC Buss and "Swept Frequency Inverter". This style usually has diodes in the rectifier (unless the design engineer wanted to use SCR's for the shutdown mode). The inverter will start at a frequency far different that the natural tank frequency. Then as power is dialed up, the frequency of the inverter is moved closer to the tank frequency, thus producing power more of the time in the tank, and thereby increasing the average power produced in the load.

Some manufacturers have used a combination of the two topologies.

Some induction units are series tuned tank circuits, some are parallel.

Then there is always the famed "Crowbar" induction units. Which usually work until the day that any one component fails, then ALL components fail at once. This type of machine is easy to troubleshoot. Step 1, replace all components, Step 2 turn the machine back on. Step 3, if Step 2 failed repeat Step 1, then replace the cabinet, then proceed to Step 2.