A musician is a person who either sings, arranges, composes or writes lyrics for songs, often they can do all 4, but there are also individuals who have specialised in 1 or 2 roles. Sometimes the director of the anime or a similar role might write lyrics or even sing on a song for the anime they are working on, but generally the musician role shouldn't be applied to them, unless they often do that on songs unrelated to anime they work on. A band is a group of musicians who create and/or perform their songs together.
====Role: Producer==== Generally a person who is in one way or another involved with creating or publishing an anime. Producer also covers writers (novels, light novels, visual novels) and should be applied to musicians who get credited for writing the music (音楽) for the anime (a person can have more than one role, if they are applicable, but this is most often the case with prominent musicians who compose entire soundtracks for the anime).