Final answer:
A wave is an energy disturbance that can travel through space, while a medium is the substance through which a wave propagates. Mechanical waves require a medium, such as sound needing air, but light, an electromagnetic wave, can travel through a vacuum.
Step-by-step explanation:
The difference between a wave and a medium is that a wave is an energy disturbance that moves through space, while a medium is the material through which this disturbance travels. Mechanical waves, such as sound and water waves, require a medium like air or water to propagate. The medium itself does not travel with the wave; instead, it facilitates the transfer of energy as the wave moves through it. Unlike mechanical waves, electromagnetic waves, including light, do not need a medium and can travel through a vacuum.
Waves are characterized by moving crests and troughs, and they can be either transverse or longitudinal depending on how the particles of the medium move relative to the direction of wave propagation. Additionally, waves can experience reflection, refraction, and interference when they encounter boundaries or other waves within the medium.