Ijāzah is a teacher’s authorization to narrate specified or otherwise qualified material; it does not mean the teacher necessarily recited every report to the student. Munāwalah is physical handover of a book or source copy. Its status with explicit authorization differs from handover without permission.
Mukātabah is written communication: the teacher writes, or has a report written, to a student. Its reliability depends on the identity of the writing, its accuracy and the kind of permission involved. Simply discovering a letter is not identical to receiving authorized transmission.
Example: A teacher hands over an authenticated copy and says, “Narrate this from me”: handover with ijāzah. Merely gifting a book is not the same as authorizing narration. These modes should not be described using unqualified formulas that specifically imply direct hearing.