The .azw(3) files are the books, but they are encrypted with DRM. The DRM is per-device/app.
I believe once a book is borrowed, you can download it through any app/device
that is signed into your Amazon account (although there is usually a 6-devices/apps-per-book-at-a-time limit).
In order to borrow the book, you will, depending on the publisher, need a device (the apps will NOT work). And all books checked out through Prime Lending Library are like this. But afterwards, it should be available from all apps as well.
Edit: I forgot to mention
-- Prime books will not be available from the apps. Just the library loans, even if it requires a device to check it out.