An EFHW is a genuine half-wave fed at a voltage point through a 49:1 transformer. This gives you the wire length, the counterpoise, and the transformer and capacitor that feed it.
A true half wave, fed at the end through a 49:1 transformer.
An EFHW is a genuine half-wave wire fed at a high-voltage point, which lets you feed it from one end instead of the middle.
The diagram shows the toroid transformer wiring and where the capacitor and wire attach — the wire simply continues off the transformer to its full length.
The transformer sees very high voltage at the feedpoint; use a core and wire rated for your power, and keep the counterpoise the length shown — too long or too short pulls it off tune.