They are not the same as a corset.

A bustier or bustiere is a form-fitting garment for women, which is traditionally worn as lingerie.

The primary purpose of the bustier is to push up the bust by tightening against the upper midriff and forcing the breasts upward, while gently shaping the waist.

In modern times it might also be worn as a push-up bra under a low-backed dress, or as a camisole for outerwear.

The bustier can also be worn as a half-slip under sheer upper garments if a bold display of the midriff is not desired.

Modern bustiers are often made with mesh panels rather than the traditional boning.

A bustier resembles a basque, but it is shorter.  It reaches down only to the ribs or waist.

You may also want to learn about the corset & tightlacing.