Lap is a grinding tool used for rubbing a brittle material such as glass against a surface such as iron or glass itself with an abrasive such as aluminum oxide, jewelers rouge, silicon carbide, diamond ets., between them.
A coated abrasive comprises an abrasive fixed to a backing material such as paper, cloth, rubber, resin, polyester or even metal, many of which are flexible. Sandpaper is a very common Flexible Hones.