Coptic binding refers to an ancient binding from Egypt which traditionally was done with wooden boards for covers. These days it is modified to have covers of board with fabrics on top. The pages are sewn linked together and then attached to the board. Its advantage is a flexible hinge that allows pages to open completely.
Japanese binding refers to another ancient method. Traditionally the pages were attached to the covers by a decorative stitch at the spine, by drilling a hole through the stack and running a stitch up and down and on the outside edge at every opportunity. It can be modified to be bound by a simple sweep of ribbon that is decorative as well.
Kettle stitch refers to a binding which has a partially open spine. The pages are sewn in a kettle link to the top and bottom of the spine pieces. Very attractive and decorative. This is a non-adhesive binding and again, the pages lay flat for ease of use.
Hard spine or traditional refers to a method of binding where the pages are sewn to each other and to the spine piece. The cover is attached afterwards. The most traditional of these choices.
Long stitch refers to a non-adhesive binding where the sewing runs up and down the spine, weaving its way through the cover itself. It can be a nice decorative element depending on the color of the cord.