composing vs arranging

composing and arranging both are nouns.

Word	Noun	Adjective	Verb	Adverb
composing	Yes	No	No	No
arranging	Yes	No	No	No

As nouns, arranging is a hyponym of composing; that is, arranging is a word with a more specific, narrower meaning than composing:

Other hyponyms of composing include arrangement, transcription, realisation, realization, recapitulation.

composing (noun)	arranging (noun)
musical creation	the act of arranging and adapting a piece of music
the spatial property resulting from the arrangement of parts in relation to each other and to the whole