Differences between a PhD and a published book
The PhD is an exam
The first difference is that you write a PhD thesis to pass an exam and gain a qualification. A published book is not a piece of exam work and it should not read like one.
Your readership will be wider and less expert
The thesis is written in the first instance for 3 people only: your supervisor and two examiners. These are all highly expert readers who know the field to which you are contributing. To them you are proving your own expertise and originality. The readership of a published academic book is, the publisher will hope, greater than three, so you consequently need to alter its style and format, to pitch it so that a wider (albeit probably still academic) readership can easily understand it.
Oh yes, a book is a commercial product
Publishers look at a manuscript in terms of its commercial potential whereas a thesis examiner will be looking at it to judge its scholarly credentials. This is an important aspect which you need to take into account.