Yes, there are books within the PHB, listed within the table and described on the next page. Since you asked why spellbooks are made out of vellum, it's important to know what it was and how it's used.
As the link describes, vellum is paper made from cow skin. Since it's made from a form of leather, it shares special properties that paper does not, such as increased durability in harsher conditions, fewer chances of bleeding, and a longer lifespan overall. More directly speaking, important documents and artworks that had to travel long distances utilized vellum to assure that the quality would last.
As a wizard relies on having a trustworthy spellbook with him during his travels, it would be wise for them to find the best option available. If they were to choose paper instead, the harsh conditions they are met with could ruin the book:
- Being submerged will definitely make the ink run, ruining their spells at the least. At most, it will disintegrate.
- Being engulfed in flames will dry out the paper and make them brittle, and easy to shatter.
The more the book is used, the more likely you'll end up severing the
bonds that the page has to the binding, while vellum is less likely
These are all advantages vellum has over paper. It has more of an ability to adapt without compromising its endurance or quality. The ink ends up tattooing the vellum more than riding it, and while the moisture might inflate the pages, they will regain the durability of leather, and dry out just as easily. (The same as rawhide can be moistened and dried multiple times without wearing out it's quality).
To address how you should describe the tomes in a library, that would all depend on what kind of tomes you're talking about. History shows us that important documents, such as religious records, were recorded on vellum, while less important documents were written on paper. The Library of Alexandria had mostly paper scrolls piled in cubicles, so adding everything together, though the majority of the books will be written on paper, you might find some vellum books and scrolls tucked away in sparse corners as well.