A headband is a clothing accessory worn in the hair or around the forehead, usually to hold hair away from the face or eyes, or to help control forehead sweat or to provide some protection to the head
Iranian king wearing headband
A hard plastic headband, or Alice band
Tartessian gold headband from the Iron Age
A bandeau is a garment comprising, in appearance, a strip of cloth. Today, the term frequently refers to a garment that wraps around a woman's breasts. It is usually part of a bikini in sports or swim
Headband
…came from the belief that the tight pressure they provided around the forehead could relieve or prevent headaches. The French called such a garment a bandeau (bandeaux, plural). In the 1910s, headache bands would likely have been more lacy in design—a crochet central panel decorated with ribbons and rosettes…
Woman wearing a bandeau bikini top
Bandeau bikini with halter strap
A 1924 Cartier bandeau made of natural pearls, diamonds, and platinum. A style of a tiara, which perched atop the hair, was adapted into this new form, mimicking the cloth bandeau fashionable women wore around the forehead.
An ancient Roman Villa Romana del Casale (A.D. 286–305) mosaic mural in Sicily depicts some earlier bandeaux.