Chiaroscuro Lighting:
Chiaroscuro is an Italian term which means light and dark and basically refers to the high contrast light/dark style used in Renaissance painting and later in photography and cinema. In modern terms Chiaroscuro means strong or bold contrasts between light and dark areas in the photograph. It is often used in studio portraits using single-point lighting to cast a shadow across one side of the subject. This means that Chiaroscuro Lighting creates a very low key image as there are a lot of dark areas on the picture.
As you can see, half of the face in the image is completely enveloped in shadow, creating a very dark and mysterious atmosphere, similar to that of renaissance paintings of which the style is based.
Rembrandt Lighting:
Rembrandt lighting is a lighting technique that is used in studio portrait photography. It can be achieved using one light and a reflector, or two lights, and is popular because it is capable of producing images which appear both natural and compelling without needing too much equipment. The iconic sign for Rembrandt lighting is the triangular light/reflection next to the nose, under the eye, on the cheekbone usually on the side of the face that is darker or further away.