Sound is a microscopic oscillation in the molecular level of a substance. Vibration is a macroscopic oscillation of structures, that is things that move, and behind all things that move, is a force that is pushing or pulling them. Vibration analysis attempts to measure this force by measuring the acceleration of a machine member with an accelerometer. Sound on the other hand is the precursor of this vibration, this force. This sound comes from among other things friction, which is an atomic force.
Friction is a generator of sound in solids as well as in gasses.
In gasses, turbulence makes the molecules collide with each other in random ways causing them to oscillate and generate sound waves. Sound in air is a pressure wave. Air molecules are moving in tight or loose bunches along the direction of propagation. Tight bunches, like a wind gast, are higher pressure where loose bunches are lower pressure. Our ear responds to these pressure fluctuations and our brain interprets them accordingly.