This portrait shows Split Lighting, it splits the face exactly into equal halves with one side being in the light, and the other in shadow. It is often used to create dramatic images for things like portraits of a band or an artist. The light is to the right side and fairly level to the subject’s face, which causes one side to be lit up and the other side to be in shadow. http://www.mmhsphoto.com/in-class-assignments.html
This portrait shows Butterfly Lighting, it is named for the butterfly shaped shadow that is created under the nose by placing the main light source above and directly behind the camera. The photographer is basically shooting underneath the light source for this pattern. It is most often used for glamour style shots and to create shadows under the cheeks and chin. http://themenofhollywood.blogspot.com/2010/07/matt-bomer-interview-with-houston.html
This is Rembrandt Lighting, Rembrandt lighting is identified by the triangle of light on the cheek. Rembrandt lighting creates that little triangle of light in the middle on the opposite side of the light. The tricky part of Rembrandt lighting is to make sure the eye on the shadow side of the face has light in it and has a catch light. Rembrandt lighting is more dramatic, so like split lighting it creates more mood and a darker feel to your image. The shadows have more contrast to them and the light it more intense to create the dramatic lighting.