Short answer
Grey is achromatic — it has no hue — so under a definition of colour that means 'a hue', grey does not qualify. Under any definition that means 'a distinguishable appearance you can name and specify', it plainly does. In practice grey behaves like one of the most demanding colours there is, because its lack of hue is exactly what makes it unstable.
Grey sits on the neutral axis, with lightness but effectively no hue or saturation. On that definition it is a tone rather than a colour, alongside black and white.
Greys are specified, mixed and compared constantly, and paint ranges carry dozens that are clearly distinguishable from one another. No practical colour system treats grey as absent.
A truly neutral grey is a knife-edge condition. Almost every grey people call grey carries a slight bias, and the visual system exaggerates whatever bias is present relative to its surroundings — so the same grey genuinely can look green in one room and violet in another.
A perfectly neutral grey reflects all wavelengths in equal proportion, just at reduced intensity. Manufacturing one is possible — photographic grey cards exist precisely for this purpose — but it is not what most greys are. Decorative greys are mixed from coloured pigments and almost always carry a small residual bias towards blue, green, violet or brown. Because there is no hue to dominate, that bias has nothing to compete with, which is why it becomes obvious at scale even when it was invisible on a small sample.
Two effects compound. First, simultaneous contrast: the visual system pushes a colour's appearance away from its surroundings, so a grey beside a warm colour looks cooler and the same grey beside a cool colour looks warmer. Second, illumination: a light source deficient in part of the spectrum cannot render the pigment mix evenly, so a grey can shift character completely between daylight and a warm bulb. Neither effect has anything to hold on to in a grey, which is why greys are the paints most often repainted.
The practical consequence: judge greys in threes, against a neutral reference, on more than one wall, at more than one time of day.
Grey's neutrality is also useful. A neutral grey card gives a camera something to calibrate white balance against, and neutral grey is a conventional background for judging other colours because it biases the eye least. Mid-grey is often used as an interface background for the same reason: it lets both lighter and darker content sit against it without the background asserting a colour of its own.
Wavelength ranges and perceptual thresholds are given as approximations: both vary between individuals and with viewing conditions, and sources differ on exact boundaries. Where a figure is contested or unavailable, this page says so rather than picking one.