One that binds — the hand or the machine that gathers loose leaves and makes them a single object. The pages existed before; the binder makes them a book, which is a different thing than a stack.
Agent noun formed on bind (Old English bindan, to tie together), naming the one who performs the binding rather than the resulting bound thing.
Names the hand or the process that does the binding, distinct from the thing it produces — the maker of the book, not the book.