A wave is a disturbance that travels through a medium, while sound may be defined as vibration that travels through a medium (such as air or water), generally in audible range (something we can hear).
Sound is a wave. We can show that sound travels in the form of waves by using tuning forks. A tuning fork has a handle and it splits into two limbs or tines. When these tines are struck on a surface, the fork begins to vibrate. As the tines contract, they create a region of low pressure (called as rarefaction) as the air expands near them. When the tines move away from their usual position, they create a region of high pressure (known as compression) as the air molecules are compressed. This series of compressions and rarefactions can be heard by placing a vibrating tuning fork near our ear. As we rotate a vibrating tuning fork near our ear, we can hear alternate soft and loud sounds. This clearly shows that sound travels as waves. The same type of interference can also be observed by placing 2 speakers a meter or so away from each other and walking by them. The interference will create some regions of loud and soft sound, proving that sound travels as wave.
The alternate explanation is that sound is the scattering of particles knocked off from the object originating the sound. Since experimental evidence fails to confirm the loss of particles, it is concluded that sound travels as waves.
Hope this helps.