"Transcription" is from the Latin for "writing across", so exactly as
folks have said it's a basically unaltered, but 'ported', version of
the original.  On the other hand, an "arrangement" takes more liberties,
matching its meaning of "(re-)organising" something.

Regarding the question about how rolls were created, have a look at the
page on my web site which considers how Aeolian recorded hand-played
performances -- which started around 1910 -- or transcribed sheet music
directly into the roll:

  http://www.pianorolls.co.uk/Duo-Art%20recording%20process.html 

Aeolian were almost certainly the only reproducing roll manufacturer
that tried to create a playable roll in real time; this included
perforating both the notes and the expression coding.  "Tried" is the
operative word: it's thought that they failed to figure a workable
way of adding the 'snakebite' accenting perforations in real time so
they punched them in later.  There are surviving 'original' rolls of
hand-played recordings, so this is fully proven with hard evidence.

Many other rolls were simply created at a music desk, commonly known
as "arranged" rolls even though, as we have discussed, many are really
transcripts.  Aeolian transcribed Pianola versions from orchestral
scores as well as using published piano transcriptions or arrangements.
Some rolls were labelled "arranged for Pianola", though, so it seems
the lack of care with the two terms is a long-standing issue!

Julian Dyer