The early waist garment was called a…

… “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)