A backup vocalist is a vocalist that sings in harmony with the lead vocalist, with other backup vocalists, or alone but in the background of a song. A backup vocalist will almost always work with a lead vocalist but the converse is not always true.
Backup singer, backing singer, background singer, and background vocalist are all terms with the same meaning: a vocalist who sings in support (in back-up) of a lead vocalist or singer, often accompanied by other backup singers.