He is a gray, probably what is known as an iron gray a year ago, a dark grey all over, as he lightens so he will go to a dapple grey and eventually white, which is still known as grey. Then as they age further many go to what is known as flea bitten grey when they gain chestnut freckles in their coat.
The horse is grey as you see. A grey horse is a horse that has the grey gene (one or two/heterozygous or homozygous) which works like a blanket and lightens the original base color, eventually to white.
Any horse with that gene can be called (and is) a grey, however since it lightens you can have multiple shades, from what looks like, say, a bay horse to a pure white horse. As you can imagine there are a lot of descriptive terms for the different shades (which is why you are getting so many responses).