The difference between a "transcription" and "arrangement" may be a
little confusing and vague but, basically, a transcription is a direct
re-write or adaptation of a work of music for a different medium than
it was intended for.

If one were to make, say, an 88-note roll version from the score of my
march, "Discover America", for example, and punch it so it was an exact
representation, note for note, of the original score, that would be a
transcription.  My own 88-note roll of the Earl Heinz classic phono
recording, "Heinz 57", is an example of a transcription.  No arranging
done there -- it is a note-for-note transcription.

When one crosses the line and gets into restructuring, re-harmonizing,
or re-arranging a work in any manner, a new arrangement has been
created.  Just compare some of the two-handed 88-note rolls with the
published piano sheet music that inspired them and it should give a
fair idea of what the term "arrangement" means.

Another good example is how arrangers were able to distill songs down
into 44-note arrangements for the early coin pianos, preserving the
most significant notes (usually) of the songs; ditto the band organ
arrangements for instruments with their abbreviated and truncated
scales.

And certainly those marvelous ragtime parodies (for example, "Misery
Rag" from "Il Misere") fit into the arrangement category of classical
and operatic themes!  I feel that Prof. Felix Arndt modestly referred
to his efforts as "transcriptions", yet the rolls contained his obvious
trademark stylistic flourishes and interpretations, certainly making
them worthy of being called "arrangements".

Stephen K Goodman - Professional Player Piano & Nickelodeon Restoration
Tarpey Village (Fresno/Clovis) California, USA
http://www.mechanicalmusicrestoration.com/