… “cotte”, an old French word for any close-fitting garment. (Today the French word cote means “next to” or “rib”). Various garment names were evolved from this: petticoat, waistcoat, etc. When the word “corset” was used, it meant an outer garment, and was not at all associated with the later application of the term for undergarments.
(Sketch: idealized drawing of “smalls” in 1500)