gray cat; grey cat
Refers to a cat with gray fur. The word is straightforward and descriptive.
近所に灰猫が住んでいる。
A gray cat lives in the neighborhood.
ash-covered cat
Describes a cat that is literally covered in ash, such as from a fireplace or volcanic ash. This sense is less common and more situational.
暖炉のそばから灰猫が出てきた。
An ash-covered cat came out from beside the fireplace.
Compound of 灰 (hai, 'ash; gray') and 猫 (neko, 'cat'). The derivation is transparent.