I have seen that sometimes an author will have one website with a lot of content and a separate website that does nothing but offer the book(s) for sale. What are the advantages of this approach? What are the advantages of having only one website, and offering the book for sale directly on that website (which would have supporting articles, perhaps some unrelated content, perhaps some interactive features, more detail about the author, and perhaps some sections from the book(s) to whet the reader's appetite)?
Often the author website is the author's own, managed by themselves. It is a place where the author blogs their private opinion, portraits themselves as a person, often with a glimpse into their private lives, and presents their œuvre. Even when the author website is managed by the publisher, the purpose of the author website is to provide a hub for all information surrounding an author.
The book websites are part of the publisher's marketing strategy for that book. They often have a crunch page to convert visits to sales. Everything on a book website is designed to make the visitor click the buy button.
If you only have one book you've authored, it's best to just have the one site based on that book. You should include free info related to the subject of the book. This is to build a following/traffic/list for the book. You should also be promoting the sale of the book at every appropriate opportunity.
By all means include author information.
When you have a second book (or if you have more than one) you should have a separate site for each book AND a separate author site. On the author site you should, among the normal author info, include a list and description/sale copy for each book with a link to that book's site.
Can this all be done on one site: YES but I prefer the multi-site version which provides better search engine optimization possibilities, especially if your books are focused on different keyword phrases. Although your books may be related in some manner, the specific, "long-tail" keyword phrases are likely to be different and therefore give you better search engine visibility.
I have four. I now profoundly wish I only had one.
The idea of a "site" is now becoming moribund anyway. The essence of a "site" is a home page, but the importance of the home page is diminishing every year simply because, across the board, home pages get less and less traffic each year. People navigate the web using search and by following links in social media. No one types a URL into a browser anymore. Thus people go straight to the page of interest, not to the "site". Having multiple sites, therefore, is just a maintenance headache and expense that is unlikely to do you any good.