كِتَابُ زَيْدٍ جَدِيدٌ - “Zayd’s book is new.” The definite idafah is the subject.
كِتَابُ وَلَدٍ عَلَى الطَّاوِلَةِ - “A boy’s book is on the table.” The indefinite idafah is sufficiently specified to be used as the subject in this context.
Both are idafah phrases, but they do not have the same definiteness.