Wave is a disturbance that propagates with respect to time through a medium or empty space. Waves are basically of two types: transverse wave and longitudinal wave.
Transverse waves are those in which vibrations are perpendicular to the propagation of the wave.
Example: Light wave in space, water wave on water surface.
Longitudinal waves are those in which vibrations are parallel to the propagation of the wave.
Example: Vibration in a spring after being released from compression or expansion, sound wave in air.
Sound is a form of energy that travels through air or any other medium as vibration and can be heard when it reaches a person's or animal's ear. Sound waves are mechanical waves.
Example: When you hit a table with your hand vibration is produced in the table as well as your hand and this vibration propagates through air and reaches our ears and we hear the sound.