The Turbo brush is indeed an air powered head, which needs no electrical wiring.
A motorhead, or power head, is one that must have an electric supply, and this is usually a long wire which runs up the entire length of the hose and metal wand. Most wires are embedded inside the hose, with connectors at each end, one end going into the vacuum casing itself and the other end going into the wand connector.
The advantage of a motor head over a turbo brush is that it isn't dependent on a strong airflow from the vacuum cleaner, but they are less reliable and more susceptible to electrical cable breakage inside the hose, or wand connectors.