Although white noise plays equally loudly at all frequencies, it fails in giving the listener such a perception, because of psychoacoustics.
One needs to pass white noise through a filter, which inverts our frequency sensitivity curve, to create grey noise, a noise that feels perceptually flat.
In other words...
Grey noise and white noise would have been the same if our ears where equally sensitive to all frequencies in the audible spectrum.
There is nothing such as a unique grey noise. "Grey noise" is a generic term that stands for a perceptually-flattened noise. The flattening curve to be applied depends on the listener’s particular hearing thresholds and the sound pressure the grey noise will play at. Our ears are indeed extremely non linear, and the perception of the different frequencies depends on the overall loudness (the Fletcher-Munson
curves). For example, at lower levels, the sensitivity of our ears toward the lower and higher frequencies drops drastically.
True grey noise doesn't exist, unless it has been created for your own hearing and for a particular sound level.
myNoise.net is the only place on the Internet that implements a genuine grey noise generator, online, calibrated to your hearing threshold levels.
In audio applications, grey noise has little purpose, but can be used to subjectively check the neutrality of a sound system.
In healthcare applications, grey noise is used to treat hyperacusis, an increased sensitivity to normal environmental sounds, or mask tinnitus, a ringing in your ear occurring without any stimulus.