Both smyth sewn and adhesive bound book blocks can be cased in with either a round back or a square back. Round back indicates the spine has been rounded and the cover is made with a paper backliner to allow the cover to follow the curvature of the rounded book block spine.
Mechanically bound casebound books normally refer to a wire-o bound book block that is glued to a hard cover. These can be both round back (this will have two separate endsheets on thicker cover stock) or square back (this will use a one piece endsheet normally on 15pt cover stock that we score in the middle to create a “V” shape when closed). We have automated processes for both round and square back casebound wire-o books. While not as common, we can also case in a book block that uses a spiral wire or plastic coil binding method.