They are not the same. A brow lift lifts the brows and the skin of the eyelids below as a result. It is generally done either through a direct incision above the brow or through and upper lid incision.
A mid-forehead lift is also used to raise the brows, but the incision is placed in the skin well above the brow hairs, hidden in the horizontal forehead creases.
A Forehead lift lifts forehead skin as well as the brows and eyelids below. Some call them a brow lift because this is the facial feature the patient wants lifted, but the forehead will be lifted as well.