Technically, a vibration is a mechanical phenomenon involving periodic motion of matter. Sound is a vibration of air, for example. Seismic waves in the Earth that cause earthquakes are a vibration of soil and rock, and the shaking caused by your electric toothbrush when you hold it are all vibrations. Indeed, temperature is only a measure of the amount of vibration associated with molecules of any substance (technically, it's related to the average velocity of molecules vibrating and also colliding in a gas or liquid — but I digress).
Vibration is a periodic phenomenon. This means that it has a frequency, a period (the inverse of frequency), an amplitude, and a phase for each of the harmonics that constitute it. Vibration also has a medium (some kind of matter) that is moving.
Wireless connections are a periodic phenomenon as well (and, like many vibrations, it manifests as waves). But unlike vibrations, wireless connections are a special kind of wave known as an electromagnetic wave. With these waves, there is no medium (no matter) and, therefore, nothing to vibrate. So, technically, they are not vibrations at all.
Instead, they are simply perturbations (disturbances) in the electromagnetic field and are caused by changes to the electrical field that then induce changes in the magnetic field that then induce changes in the electric field again, and so on.
They are, therefore, just a different variety of things like light, x rays, radio waves, and an entire spectrum of electromagnetic waves.
So, they are very similar to vibrations, but technically they are not the same physical phenomenon.