Which Grey?

I have been doing some fairly simple, neutral coloured design assignments of late so have been exploring different types of greys. There are three main types- pure greys, warm greys and cool greys. Pure greys are of course just tints of black. Warm greys are greys with a slight cast of either yellow, orange or red and cool greys have a slight cast of either green, blue or violet. Here is an example picture from Wikipedia.

This image made me wonder though that we could think of these swatches in two ways- as greys, or as simple super dulled down colours. When you compare warm greys and cool greys with pure greys they hardly look grey at all! They look colourful! Tricky colour terminology...