In old radio programs we often hear the phrase, "The following program
is transcribed...," meaning it is recorded to electronic transcription
disc (ET) or other recording medium for broadcast at a later time,
rather than a live performance.  Another source of the meaning of terms
is Norton/Groove Concise Encyclopedia of Music.  This is a single volume
version (not the 20-, now 29-volume, original) edited by Stanley Sadie.

Arrangement.  The reworking or adaptation of a composition, usually for
a different medium from that of the original.

Transcription.  Term for a written copy of a musical work involving
some change.  It may be a change of medium (thus meaning the same as
'arrangement'); or it may be that its notation has been changed (e.g.,
from tablature to staff) or its layout (e.g., from parts to score).
The term may also include the writing down of music from a live or
recorded performance, or its transference from sound to some graphic
form by electronic or mechanical means.

I would take it from the above that while a musical performance on a
piano roll may be an arrangement, it is certainly a transcription.

Don Shenbarger