Formal:
* Arrangement: This is the most common and straightforward term.
* Transcription: This implies a more literal transfer of the music from one instrument to another, often with minimal changes.
* Adaptation: This implies a more significant change to the music, perhaps changing the style or adding new elements.
Informal:
* Version: This is a general term that can refer to any variation of a piece of music.
* Setting: This is often used when referring to a specific instrument or voice, like "a piano setting of the song."
* Reworking: This emphasizes the act of significantly changing the original music.
Specific to the instrument:
* Piano reduction: A simplified version of a work for piano.
* Orchestration: An arrangement of a piece for an orchestra.
* Choral arrangement: An arrangement of a piece for a choir.
The best word to use depends on the context and the specific changes made to the original work.