There is a http://www.qplussizelingerie.com/ similar type of lingerie/sleepwear known as the babydoll. Both terms describe short, loose-fitting, sleeveless fashions. Typically, though, babydolls are amassed loose-fitting at the hips and are generally examined to more resemble a blossoming girl's nightgown (although many cutting edge varieties only vaguely follow this definition adding various sexualizing countenance which, of course, would only be appropriate for an adult).
The corset is a garment that defaulter undergone manifold changes over the years. Originally, the garment we now know as the corset was patent as stays in the early 16th century. It was a simple bodice, with tabs at the waist, stiffened by horn, buckram, and whalebone (Steele 6).