As a NES, but not a teacher, I would offer my understanding of the subtle difference:
When I used to commute, by train, into London, I would regularly find a quiet spot in the corridor and dictate telexes (in those days) into a small hand-held tape recorder, for the secretary to transcribe as telexes the next day.
I might also have drafted a handwritten response to a letter and the secretary would transcribe my handwritten material into either a formally typed letter or a telex.
In the case of dictation, a person actually dictates the information to the person recording, in writing, the text concerned. Transcription means transcribing information from one [storage] system to another.
dictate - definition of dictate by the Free Online Dictionary, Thesaurus and Encyclopedia.
To say or read aloud to be recorded or written by another: dictate a letter.
transcribe - definition of transcribe by the Free Online Dictionary, Thesaurus and Encyclopedia.
To make a full written or typewritten copy of (dictated material, for example).
Hope this helps