It is a "lighter" shade of brown, but on the cool side, without reds, or warm tints. Ash brown refers to the "gray" tint of ash (not the "black"), not silver gray you get when you get old, but a slight tint of gray. And no, there's no "black" involved.
Ash has a green tint which disallows redish mousey tones to appear in brown. It is more dusty than gray.