Book module versus Taxonomy module
The difference is that the Book module defines a content type ("Book page") that can be used to create books. The Book module allows also to create a hierarchical structure, and it shows:


the list of the child pages associated with the current book you are visualizing 
a menu that allows to pass from a page to the next one, the previous one, and the top one
a link that allows you to create a new child page
a link that allows you to see a printable version of the current book page




The Taxonomy module is used to categorize the content of a site, but when you click on the link of a taxonomy term used by a node, the page you see shows all the nodes using that taxonomy term, without allowing you to pass from a node to the successive, or the one hierarchically on the top.

Said in sort, the Taxonomy module handles an attribute (in Drupal terminology is a field, handled with the field API) that can be associated with nodes, but also to users, while the Book module defines a content type that can be used to create books, and allows to handle that content type in a hierarchical way.