difference between radio and sound waves
A radio wave is an electromagnetic wave and so too is light. Generally a lot can be said about waves (electromagnetic waves, sound waves, water waves). What characterizes a wave is that they all satisfy the wave function f = f(x±vt) and therefore also the wave equation. So from a mathematical point of view all these waves are similar.
One major difference is that a sound wave is longitudinal while a radio wave is transverse. In air, a sound wave represents the longitudinal displacement of the air molecules, or the pressure of the air. An em wave is more subtle to explain. It consists of electric and a magnetic field components and these components are orthogonal to each other. Em waves also have a polarisation. In satellite communication the waves have a circular polarisation while radio waves on the earth most often have a linear polarisation.
Another major difference is that an em wave needs no medium to travel while a sound wave needs some medium (for example air, water). In vacuum em waves travel with the speed of light while a sound wave wouldn't propagate at all.
The concept of waves comes from the underlying mathematics for different physical phenomenas. Everything can be characterized by a wave, even YOU! To explain how two waves (any type of wave) interact with each other the wave concept is really powerful. However, the wave concept does not explain all the physical phenomenas. The wave concept explains how energy and momentum is transported through space but doesn't explain how matter is transported. Electromagnetic waves has both a particle and a wave nature. To explain how these particles are transported (photons) another model is needed, and this is called the particle model.