A choir is a group of people singing together. You would sing in a choir.
A chorus is the repetition at the end of each verse sung by everyone, whereas the verse will be sung by a soloist. However, it is also a group of people performing with an orchestra.
The adjective is choral.
Speaking as a choral singer, I'd add that a choir can include a 'semi-chorus' - a few people who sometimes sing in a smaller group (within the main choir). A few people who sometimes sing in a smaller group separate from the main choir is often called a 'chamber choir'.