There are various names for groups of singers. As for traditional pieces of music, the type of music you'd generally think of to accompany are religious ceremonies; the word "choir" is going to be the most popular actually.
It isn't always an accurate name to name a group of singers. Though if the performance will be held outside church, then the word "chorus" is what often used. Choirs have different sections and they are often deemed as choir themselves. To give you an example, brass choirs are part of a larger orchestra of choir. There are different voices that are referred to different choirs too. For instance, baritone choir and tenor choir are parts that are forming the overall choir though, they typically work off different music sheet.
On the other hand, a conductor is the one who is leading the choir. The most recognizable part of choir, he/she is often seen using his hands and varieties of prompts in guiding the choir throughout the entire score that prompts different music speed together with prompts for different parts of choir to be involved. Vocal chorus has a tendency to be divided into 4 different parts. This does not have to be the standard format though. In most cases, composers are insisting that a great number of choirs are used and might deviate as well from normal format of the choir. Some of the composers are known to expand choirs beyond the normal ranges as well as pen pieces that is in need of any number of sections of voices and different voices too.
Combining the performance with music is something that'll different from one composer to the other. In most cases, the music is sung unaccompanied, in its purest form. The choice will be made by the composer. He/she has plenty of decisions to be made. To give you an example, the arrangement of choirs, some composers will be insisting to arrange the voices within the choir from right to left, moving from lowest voice to the highest voice. At times, the composer prefers splitting the choir by age or sex, with boy choirs being separated to adult choirs. Some are also arguing that the parts have to be close to each other to make sure that their voices will stay tuned. However, composers always endeavor to do what's right for the music.
As soon as you reach upper echelons of ability in choir, the voices have the tendency to mix with each other to their own regards. Not having backups for similar voices around means that one's confidence and ability needs to be at high level and this type of arrangement is favored rarely by composers who are working with anything but skilled and seasoned vocalists. Some are even arguing that freely formed choir is losing some of its sound quality that is associated with the traditional choral arrangement.
The probabilities of choir arrangements are literally endless and usually, the thoughts of audience are taken into account when final decision is made.