As I see it, there are four types of arranging, based on how far your arrangement takes you from the source material.
Transcription is the art of copying down exactly what is already in existence. You might be called to write an arrangement for a cover band, or for a soloist seeking a performance true to the original. The voice of the arranger is hardly present in a transcription.
Translation is the art of adapting the song to a new orchestration – writing an a cappella arrangement of a Joni Mitchell song, for example. There is much room for creativity in how you achieve this – choosing instrumentation/voicing, key, solos, form, introduction, and on and on. But the spirit of your arrangement reflects the spirit of the original version of the song. The voice of the arranger is present but secondary to the composer’s voice in a translation.
Transformation is the art of completely reimagining a song in a new context. Not every song is ripe for transformation, but when it works, it offers striking new ideas about the song’s meaning. Consider The New York Voices’ transformation of Simon and Garfunkel’s “Cecilia.” It tells a new story, one that, to me, amplifies and clarifies the original. The voice of the arranger is primary in a transformation, in dialogue with the composer’s voice.
Composition is the art of arranging when the melody is one’s own. This can be a new interpretation of a previously performed song, or a brand new composition that requires arranging decisions. The voice of the arranger and the voice of the composer are the same in a composition.