Trying to find this answer is so difficult that I can't even tell whether What is the difference between a transformer and a coupled inductor? is asking the same thing.
Some reading suggests that a "flyback" element (which may be called a "flyback transformer," may also be called a "coupled inductor?," and which may be (or always is?) part of a "flyback power converter") is at least schematically equivalent to something like a conventional transformer with a parallel inductor. Is that correct, and if so can someone provide the appropriate schematic?
Can someone provide a clear depiction of the physical embodiment of a flyback element? I can't determine what the core must look like. As far as I can decipher it consists of two independent "high-side" windings, and a low-side winding (which with a ZVS driver may actually consist of a split/dual winding).
Finally, what are the relationships between the windings, low-side current, and high-side voltage and current output characteristics?
adding to Sparky, the specific meaning to "flyback" with TV or cathode-ray tubes is that the electron beam that was scanning left-to-right across the screen will quickly "fly back" from right to left to begin the next scan line.
this beam was steered by coils mounted at the electron gun that was shooting electrons at the phosphor screen. the electronics that was connected to these coils had to generate a sawtooth waveform to determine the instantaneous position of the electron beam. this sawtooth waveform was also fed into the high-voltage transformer to get the 25000 volts necessary at the screen of the canthode ray tube to draw the electrons from the electron gun. it was during this "flyback" that the slope (or derivative w.r.t. time) of the sawtooth waveform was much greater and the result was a high voltage in the secondary winding induced by a rapidly changing current in the primary. that's why the transformer was called the "flyback transformer" in these old TVs.