There is confusion about veils. A veil is defined in the dictionary as a piece of fabric worn over the head OR face. Most people probably associate it with the see-through face coverings worn by brides, but "taking the veil" (becoming a nun) refers to the head coverings that used to be traditional in religious orders. The faces were usually exposed.

Muslims use two separate words. A hijab covers the head and hair. A niqab covers the face except the eyes. (A burqa is a full-body covering with only the eyes exposed.)