All it takes to be a composer is to write a melody. Everything else -- the chords, the harmonies, the structure, the key, the countermelodies, the bass line, the intro, the outro, and anything else you can think of is "the arrangement".

Sure, some composers, especially those with classical training, are their own arrangers. But in the theatre world and in the pop world, there are usually one or more folks hard at work shaping the music and creating all of the elements of the music that aren't the actual melody. And to further complicate matters, sometimes the composer is actively involved, sometimes they're disinterested, and sometimes they're dead. That last category in particular doesn't give a lot of feedback.

Here's my favorite metaphor: if this were the world of art, all the composer would have to say is "I imagine a tree". Of course, they may or may not give you other information: "it's a pine tree"…"it's in a forest"… "it's winter". It's up to the arranger to fill in ALL of the remaining details of the black-and-white sketch to create something that is ready for viewing. (And to further the metaphor, it's the orchestrator who adds the color).

(Side note: it was common practice to refer to Orchestrators as Arrangers back in the heyday of the recording industry - think Billy May, Nelson Riddle, etc. - but nowadays, at least in the theatre world, these are distinct jobs).

Amongst arrangers, it's generally accepted that there are four distinct kinds of arranging:

1. ‍Vocal Arranging -- just like it sounds, this is figuring out what people are singing if they're not singing the melody. To me, AnnMarie Milazzo (Spring Awakening) is the undisputed master, and she does it, amazingly, without reading or writing music -- it's all by ear. Astonishing. Of course, Choral Arranging (meaning writing specifically for a choir) is a related field, and like vocal arranging, works best when there's a real understanding of the human voice.
2. Incidental Music Arranging -- figuring out underscores and transitions. This requires a keen sense of the dramatic pacing of scenes, as well as understanding how to tailor music to 'how long does it take the set to move?' Usually, the themes are drawn from the composer's melodies, but there are all sorts of compositional tricks that can be used -- reharmonizing, re-shaping, fragmentation, turned melodies upside down.‍
3. Dance Arranging -- this is a biggie, especially for me. The Dance Arranger is the liaison between the composer and the choreographer. In the simplest terms, it's shaping the music to complement the visual. The relationship of the choreographer to the dance arranger is one of the most symbiotic and collaborative in all of theatre. Like the Incidental Music Arranger, you're using every compositional tool in the book, and when it's at it's best, dance music becomes an essential part of a show and its storytelling. Think the 'Carousel Ballet' or 'Small House of Uncle Thomas' both written by Trude Rittmann, using bits of Rodgers' melodies here and there. Or Peter Howard, not John Kander, wrote 'The Hot Honey Rag'. ‍
4. Song Arranging -- a truly broad category that essentially covers all of the songs in a score. It often includes elements of all of the other arranging jobs, especially vocal arranging if, say, the song is a duet. But a deep understanding of dramatic and storytelling needs is essential.

There is a huge amount more to be written about this, but suffice it say that the terminology is insufficient. I've often just used the term "Music Arranger" or "Score Adaptor" when I've done a show where I've touched every aspect of the shaping of the music.