"The book is not a student."
Translation:Liber non est discipulus.
No, both liber and librum can be translated as 'a book' or 'the book'. The difference is noun case, how the noun modifies the sentence.
liber is the nominative singular form. It is used as the subject of a sentence (such as it is here).
librum is the accusative singular, used by most verbs as the direct object, the thing being acted on.
liber discipulum habet -> 'a/the book has a/the student'
discipulus librum habet -> 'a/the student has a/the book'