Flexural waves: the particle movement is perpendicular to the propagation direction of the wave.
Longitudinal wave: the particle movement is the same that the propagation direction of the wave.
Vibration: solid medium. There are two wave types, but the main amplitude is in the flexural waves. The vibration is characterised by the particle displacement amplitude, the velocity amplitude or the acceleration amplitude in the system.
Acoustic wave: air medium. It is characterised by the compression and expansion in time and in space. The main movement is in longitudinal waves. The acoustic field is characterised by the particle pressure and velocity.
Acoustics is a particular case of vibrations in the air. Therefore, in any vibrating system surrounded by air, certain vibrating energy is transmitted from the solid to the air (acoustic radiation). In the same way, any sound wave excites the average solids that surround it.