What is the difference between an arrangement and a transcription of a musical composition?

In the context of musical composition, the terms "arrangement" and "transcription" are often used interchangeably, though they carry distinct nuances regarding the level of creative intervention involved.12

• Transcription is primarily the adaptation of a composition for an instrument or ensemble other than those for which it was originally written. Historically, it often implied a faithful transfer of the original material, though it could also involve virtuosic elaboration, such as the piano transcriptions of J.S. Bach’s works by Franz Liszt or Ferruccio Busoni.21
• Arrangement involves a similar process of adaptation but typically grants the arranger greater freedom to modify the original score. An arranger may embellish or simplify the melody and harmonic structure to suit a specific medium, such as a jazz or rock ensemble. In these genres, the arranger essentially "improvises on manuscript paper," manipulating the original material while ensuring the source remains recognizable.21

While these definitions have evolved and sometimes reversed over time, the fundamental difference lies in the degree of liberty taken with the original musical elements.12