I don't know a huge amount about flying these, apart from a small soft kite bought for my daughter. Single Line Kites are a huge area by themselves - many people still class this as 'real' kite flying - all this multi-line stuff is cheating! I don't claim to be an expert on any of this (even less that anything else here), but I hope to learn more.....
Go to any kite festival and you will see fantastic static kite displays in the sky. Some of these kites are huge and formed into wonderful shapes and designs, often with secondary kites (or Drogues) trailing off the main flying lines. Each class of design has many sub designs and variants - these really are the beautiful kites that exist only for pleasure.
Apart from the basic children's kites and static display kites there is such a thing as kite fighting - these use single line kites that are traditionally made out of bamboo and tissue paper (modern version can also be made out of Mylar or Ripstop Nylon) and are flown around the sky just using a single line. The idea is then to damage the opponents kite - in some circles the kite lines are coated in ground glass so that you can cut the other kite's line. I hope to try this one day (at least how to control the direction of a single line kite) - it sound fun! Just don't fly a glass coated fighting kite anywhere near other kites - you won't be popular...............
And I'm sure I have missed some other single line distinctions as well!
Virtual Kite Zoo