A grass marker (or flat headstone) is flush with the ground or lays flat on the ground. The stone usually measures 4 inches thick and can be set above the ground or to lay flush with the ground. Some cemeteries only allow for flat or grass markers.
A bevel (or hickey) headstone sits flat on the ground and has a two inch slope between the front and back of the face of the stone. Hickey headstones are typically six inches in the back and four inches in the front. Hickey headstones are not typically place flush with the ground and are not a substitute for a flat headstone.