Why are there different types of winglets?
Winglet design is driven more by marketing than by engineering, so every aircraft brand tries to cultivate their own, supposedly better, shape.

A study by Nita and Scholz (PDF!), Chapter 6 gives a good overview over recent winglet studies. A raked tip performs better, and if winglets could point downwards, they also could do better. As they are, they give only 28% to 38% drag reduction of an equivalent span increase.



Raked wingtip of the Boeing 777-300