The missing-link between corset and corselette from 1914
The corselet was originally a piece of armor, covering the torso; the origin of the English word comes from cors, an Old French word meaning "bodice". The corselet as an item of women's clothing began to gain traction in 1914, as a substitute for wearing two separate pieces (a bra with either a girdle or a corset). The bust uplift cups were first introduced in 1933, but did not become common until 1943. 
A corselet was released by Warner's in 1955, named after The Merry Widow, a 1905 operetta that has been adapted several times into feature-length films. This new design featured demi-cups and a shorter girdle than its predecessors. This type of lingerie is also known as a torsolette, and is used in bridal lingerie, much like the bustier.
The original merry widow was a corselet incorporating slim panels of black, elastic yarn netting. A heavy-duty zipper was inserted behind a velvet-backed hook-and-eye flange, and the entire garment was lined with nylonvoile. Nine long, spiral wires were encased in black satin.
Lana Turner is reported to have said, "I am telling you, the merry widow was designed by a man. A woman would never do that to another woman."
Around 1960, tights and trousers began to replace corselets. However, Maidenform and other mainstream lingerie and undergarment manufacturers have sold corselets as "control slips" since around 1975.