A blade coating is a layer bonded onto a knife blade's surface, where a finish such as stonewash or bead blast only textures the steel. Boker defines a coating as a firmly bonded layer applied to the surface of an object. Black oxide is an exception: Kershaw and Gerber call it a coating, yet Kershaw says a chemical bath converts the surface of the steel to magnetite.
A knife spec sheet can print PVD coated on one knife and stonewash finish on the next without explaining the difference. A finish such as stonewash or bead blast applies nothing: the steel's own surface is scuffed or blasted. A coating puts a layer on top.
The labels are loose. Boker calls PVD coating a finishing method, Kershaw calls its BlackWash, which may be DLC or black-oxide based, a finish, and the Hogue Extrak in the grid below prints Cerakote finish. Judge by the mechanism, not the label.
Hardness claimed for a coating belongs to that surface layer; the steel's own hardness is set by its alloy and heat treatment, and the Steel Lab profiles the alloy.
Kershaw says of its own coatings that "in time, all coatings will show some wear", and Gerber says rubbing on a sheath or pants pocket will wear its black Teflon or black oxide coatings through over time.
Sharpening removes steel at the edge and any coating on it, so a freshly sharpened coated blade shows bare steel along the edge. Kershaw says it cannot recoat a blade, even for a fee.