"Jorts" is a slang term used to describe jean shorts. People used to cut off the legs of their jeans to obtain this look.
As time passed, however, clothing companies began producing a wide variety of jean shorts, and they have became popular with all ages. They come in all colors and lengths and can still be made at home by cropping a pair of jeans.
"Norts" is the slang term used to describe athletic shorts. These shorts are popular with athletes and school-aged children. Norts also come in many colors and styles, although they are typically shorter in length than other shorts.