The Pope Speaks lags even further behind. It concentrates completely on materials attributed to the Pope himself, but it does include minor and harder to find messages. This is a pretty common misunderstanding. Access points for titles and authors are chosen and verified at this point also. Subject cataloging involves selecting the subject headings appropriate to the book.
Classification is usually the final step in cataloging.
It isn't unrelated to subject cataloging, particularly when both Library of Congress Classification and Subject Headings are being used. However, when classifying a book, you can only assign one number and that presents its own challenges. Instead, they've been assigned six-digit numbers that determine their order on the shelf. The reason is to conserve space. When books are classified, it's necessary to continually reserve a certain amount of room on each shelf for interfiling new books on the same subject.