Why are there different types of winglets? If all winglets serve the same purpose (to reduce vortex drag), why do different aircraft have different winglets? This question is not trying to get a comparison of the development of winglets/wingtips, with other aircraft components, as the question of @Manu H is.
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