Confused about FB versions

These are not separate versions. It is all Facebook. The differences on how you want to present and promote your book.

A fan page is made by fans who really don't have ownership or control. E. g. if you're a fan of, I dunno, Lucille Ball. There are tons and tons of fan pages for I Love Lucy and its incarnations. Her estate probably doesn't have an ownership interest in any of them.

A business page is made by you, the owner/rights holder to promote your business. You will presumably have the best quality control over the postings, the promotion, the messages, etc. At a certain # of followers (I think the number is 50), you can get some metrics from Facebook. They are things like not only number of likes and shares (which everyone can see), but also number of views, plus you can better trace where the shares go (e. g. if they are shared again, etc.). You can see engagement, too, which should give you a better idea of which types of posts are seen/shared/liked/commented on/etc. by the most people, and you can adjust your message accordingly.

What does your publisher say?

I don't have a publisher, except myself, book is thru createspace and Amazon. It's a book on screenwriting and thus a rather narrow market. I have FB since 2010 but never really played with it. I also have considerable credits which will help me sell them, I taught at UCLA extension and also 35 years of real screenwriting experience with over 19 movies made.

What I don't understand is how a Business Page is different than the normal FB page which I have. I assume I just create a new page in the "share" area? I've spent at least a week or so trying to understand this.

Maybe it's so simple I'm just complicating it?

You may be overcomplicating things.

Use your regular account, and make a separate page for your book.

Why do you want to do this? Because your pals from High School and other FB friends are likely not fans of your book, and most likely don't want to be marketed to.