Wireless and radio : when is 'wireless' called 'radio'?

Wireless is the generic term for any transmission that is made without using wires between points, although it frequently is used to describe radio it also covers photophone, induction and broken wire systems.
Radio is the term used first in the USA, derived from radiation - the principle that governs radio waves.
It's a characteristic of all electromagnetic waves that both the electric signal and the magnetic field that accompanies it cycle many times a second. Think of a cork on a pond - as waves pass it, it goes up and down.
The frequency of the wave is simply the number of times per second the cork goes up and down as the peaks and troughs of the wave pass it. Electromagnetic waves cycle a lot faster than this, and are measured in Hertz, where 1Hz is one cycle per second.
The wavelength is the distance between each consecutive peak or trough, so if you multiply the wavelength by the frequency, you get the speed of the wave. A 100Hz wave with a wavelength of 1 metre travels at 100 metres per second.
Radio waves travel in straight lines, so theoretically no radio station should be able to transmit much farther than 40 miles because of the Earth's curvature. This is the case for television and cellphone transmissions in the UHF waveband, although a natural effect of the earth's atmosphere allows lower radio frequencies (or longer wavelengths) to bounce back and travel around the world.