composing: creating musical works
arranging: reworking existing musical material
Benny Goodman composed "Sing, Sing, Sing"
William T McDaniel arranged "Sing, Sing, Sing" for Marching Band.
transcribing: transferring music from one medium, or key to another
J.S. Bach composed "Toccata, Adagio, and Fugue in C Major" for organ.http://www.youtube.com/watch?v=FilzIfTf8O4
John P. Paynter transcribed it for the United States Army Field Band.