The Book View GUI is meant to provide basic editing abilities. Some things it does ok, some things not so good. div tags are something it doesn't do well.
The heading buttons + p button operate on the block element you are in, like the left/centre buttons. The Bold, Italics, etc. operate on the selection. So if you just click in the middle of a word and then click Bold, nothing happens - because you haven't selected any text. But if you just click in a word in a paragraph/div and click h1 then the containing block will be converted to an h1. Or a p if you click p.
The point of the heading+p buttons is really just to convert a line/paragraph from a heading to another type of heading or back to a normal paragraph.
If you are using divs, its best to use Code View.
Also note with Clips that they are really only best used in Book View for spans or other non-block elements - what you use on selected text. Trying to use a block level clip like p or div on a paragraph gets a bit messy as it deletes the existing block tag as it can't really tell where you are.