Lenses are measured in length and width. The type of lense needed depends on the scene to be shot. The different types are defined by an optical property called the focal length of the lense.
Standard Lens - roughly approximates the perspective that can be seen by one human eye. A lens with a focal length of 45mm is considered normal. A normal lense is suitable for a mid shot, but not for a close up.
Macro - these lenses range from 60-200mm. It zooms to detail a human eye cannot see. It approximates a perspective a human would see through a magnifying glass. The larger the lense size, the smaller the object that can be captured.
Wide Angle - lense equal to or less than 35mm. They are used to capture a wide view that cannot be captured by a normal lense. Fish eye lense is considered a wide angle lense, since it captures the view in a non-typical rectangular shape.
Telephoto - A lense that can be adjusted to zoom in like a telescope. The camera is placed very far away. It can create a sense of singling out a subject, but narrow down on a subject from afar.
Prime - a lense that cannot be readjusted with zoom, and camera needs to be moved to change the view.