The patterns are as follows:
any of these can be photographed "Broad" or "Short".
Here are a few examples (with recommendations about where to place the lights):
In a butterfly lighting set up the light is placed high above and in front of the subject, creating a shadow under the nose that resembles the shape of butterfly wings. This lighting is also known as Paramount Lighting or Beauty Lighting.
In Rembrandt lighting the key light is place up above the subject and at a 45 degree angle. The pattern to look for is an inverted triangle of light under the eye. The goal is to have the shadow from the nose touch the shadow on the cheek. This style of lighting is named after the Dutch painter who was known to use it in his paintings.
Loop lighting is one of the most commonly used patterns and flatters most all faces. It is created when the key light is at an angle to the subject- as to make a small shadow extend past the nose. You need to be careful that this shadow doesn't touch the upper lip. Also, if it meets up with the shadow on the cheek- you're close to Rembrandt territory and it's not a confident loop.
Split lighting is achieved when your key light is to one side of your subject, leaving the opposite in the dark. You can fill in the shadow on the opposite side of the face with a fill light, making it less intense- if you desire.
All of the above patterns of light can be photographed "Broad" or "Short." Essentially, the two terms: Broad and Short, refer to the side of the face that is more visible to the camera. If the side of the face that faces the camera is in shadow- then the images is considered to be Short Lighting but if the side of the face that is directed towards the camera is completely lit up- then it's Broad Lighting.
Here are a few examples: