jacket : Sometimes used as another term for dust jacket, a protective and often decorative wrapper, usually made of paper which wraps around the binding of a book

Fair : is a worn book that has complete text pages (including those with maps or plates) but may lack endpapers, half-title, etc. (which must be noted). Binding, jacket (if any), etc., may also be worn. All defects must be noted. (defined by AB Bookman's Weekly)

Brodart : Generally used to refer to a clear plastic cover that is sometimes added to the dustjacket or outside covering of a book. The name refers to the company by the same name which produces many book repair and archival products.