Cover
Also called book cover
The outside of a book, which protects the text block: two panels joined by the spine. Its faces are numbered: the front cover (first cover) is the outside front, the inside front cover (second cover) and the inside back cover (third cover) are the insides of the front and back panels, and the back cover (fourth cover) is the outside back. Some covers also have flaps, folded inwards.
In practice
Make the cover file last. The width of the spine depends on the page count and on the paper of the text block, so it is only right once both are settled. Then ask the printer to calculate the spine and to give you the dimensions of the cover laid flat.
The cover is specified apart from the inside, with its own paper and its own printing: it has its own line in a book’s specification. On a paperback it is usually a single piece of heavy paper, glued to the spine of the text block; the front cover, the spine and the back cover are on the front of the sheet, the inside front and inside back covers on its reverse. Say in the quote request whether that reverse will be printed and whether the cover will have flaps: both change the sheet needed.
On a hardback, the cover is usually made of two boards attached to a spine, then covered with printed paper or cloth. A dust jacket is not a cover: it is a removable wrapper fitted over it.