How do I transfer a book on my iPhone to my iPad?

If your book was downloaded to Apple Books, you will likely need to download the book from the original source to your iPad.

Books downloaded from Apple, paid or otherwise, are permanently associated with your AppleID account; paid books are available for download onto any of your Apple devices, signed-in with the same AppleID, without additional cost.

Any PDF Files that have been downloaded to the Apple Books App can be saved to files if needed - and then simply transferred to other computers. To do so, access your Apple Books Library and select PDFs. Each PDF icon will have an associated ellipsis icon (“…”); tap to expose an Action Menu - and select either Save to Files or other appropriate Share option.