They can be born any color (chestnut, bay, black, roan etc,) but they have the graying gene. Which causes them to turn white. Think of it like mixing white paint with any other color. You just keep adding white and eventually ANY color will turn white. It's kind of like that.
Gray horses are called gray because they have the graying gene. So any horse that is called white or flea-bitten or dapple gray are all incorrect to an extent. They are gray.
Gray horses go through the following phases: the color they were born - steel gray - dapple gray - white - (and some horses will become flea bitten and some just stay solid white).
Also, there are no albino horses. All horses that are born albino have an intestinal disease (that is caused by the albino gene in horses). I don't know the full extent of the disease but I think their intestines aren't fully developed or something and they will eventually die, if not put down.
I thought I might add that since gray horses are born a color such as chestnut their skin is not pink (unless they have/had a sock/white marking on their face when they were born, in which case the skin under the white area would be pink) their skin is black.