We use Shawl, Stole, Wrap and Scarf interchangeably but they really mean....
Shawl
A shawl is a piece of fabric draped over the shoulders or wrapped around the body. It is worn for decorative purposes (to accent an outfit or cover bare shoulders in formal attire), religious purposes, or to keep warm. In past shawl was used for winter only and were made from just pure wool. Shawls are typically in 30 to 45 inches wide to 70 to 85 inches long.
Stole
A stole is more of a formal shawl, made of more expensive fabric, used around the shoulders over a ball gown or formal dress. Stoles are typically narrower than a shawl. Stoles are wrapped and carried about the shoulders or arms like a cape. Stoles are made from lighter materials such as silk and chiffon.
Stoles are typically 20 to 30 inches wide to 68 to 74 inches long.
Scarf
Scarves are a long and thin piece of cloth that is wrapped or tied around your neck for warmth. Some scarves are designed to be used as a stylish accessory.
Scarves can be casual or formal and everywhere in-between.
Size of scarf normally varies from 4 to 16 inches in width and 50 to 80 inches in length.
Wrap
A wrap is a more recent term and used primarily to describe both stoles and shawls.The term wrap is a word that refers to a cloth that loosely covers any outer garment, and that can be wrapped around the upper body.