To answer your question: seems to be intended as is expressed in iPad/iPhone Users Guide, iOS version 11.4. An excerpt in the picture below (yellow highlighting is mine):
This good description is now almost vanished in the recent version (not as explicit as this one).
As for storing locally, on the iPad, you may watch/compute/verify as follows:
1) Verify a book download: Go to
Settings -> General -> iPad Storage -> Books and click to the right and see two items, there, Documents & Data and dully note the size of these.
2) Add a new book: (download a new one) and check/verify/note the new size as in previous point.
Note the size should be >0; if equal zero could be something else wrong.
3) Turn off the wifi from
Settings -> Wifi
4) Verify again the size as in 2) Should be the same.
5) Open the Books and manage your download. See the picture below:
Now, please observe three dots to the right and under the book icon. Click on them and choose what to do with the book: add to Collections.
6) Also in Books: Click on
Library icon on the lowest row of the display. This will open the Collections page. Click/tap on Collections word and choose from the pop-down listing. You should have a menu item
Downloaded where all downloaded books should take place.
7) Verify the iCloud storage occupied by your books: in
Settings -> [your name] -> iCloud -> Manage Storage -> Apple Books -> Documents & Data. You may have more than a single item
If the size here is smaller or equal than the size found in 4) for sure you have booked stored locally.
Note the size may vary, after some time some books will be reloaded to iCloud if no activity on them.