Difference Between Velomitor and Accelerometer?

An accelerometer generates a voltage signal proportional to acceleration (a = dv/dt). Bently-Nevada's Velomitor is actually an accelerometer with a built-in integrator circuit to generate a voltage signal proportional to velocity (v = dx/dt).

By contrast, a "normal" vibration probe such as Bently-Nevada "proximitor" probes generate a signal proportional to distance (gap) between the probe tip and the rotating machine's shaft.

To summarize:

Proximitor vibration probe: x

Velomitor probe: dx/dt = v

Accelerometer probe: d2x/dt2 = dv/dt = a