I know this is a bit late but I hope you see it
So there are quite a few different breeds of fantails.
- Indian fantails
- American exhibition fantails
- English exhibition fantails
- German exhibition fantails
- Syrian fantails
- Thai fantails
- Seljuk Fantails
- English garden fantails
Theres probably more but this is what I am familiar with. I breed fantails and have done for many years now. I do it as more of a hobby than anything (along with all my other birds) and quite enjoy keeping my line going. I cross a lot of the breeds together to see what I get and some of my young are gorgeous, if I do say so myself.
Anyway I currently have Indians, English exhibition, English garden and German exhibition fantails. There is a difference between all of them. Obviously as everyone has already said Indians have the crown and feathered feet, and Americans have the arched back with their heads touching it. English exhibition fantails are similar to the American only smaller and I believe the American was originally bred from these. I'm unsure if the Americans can have feathered feet or if that would be and Indian cross, however I do not breed them so I couldn't say. The German exhibition fantails again are similar to the other exhibition fantails but their heads do not go as far back and they are a lot taller in the leg. The person I gained them off claimed that they should at least have 36 tail feathers. English garden fantails are the basic white fantails (can come in other colours, just most common is white) that live in people gardens and are miss-sold as doves. They have a much straighter back and are much more able at flying, they are not a show breed and more of a utility breed. Although their job is too look nice in a garden so they still are quite showy. The seljuk and Thai are both vary rare outside of their own country's and have little knowledge on them myself. The Thai I believe is very similar to the Indian in appearance but only comes in white, the Seljuk is from turkey and is quite small, slightly resembles the English garden fantail in body shape but only has two colours. Powder blue bar and black and white. Syrian fantails are growing in popularity, yet they don't really have much to their tails so I'm afraid they have never interested me, but never say never.
Hope this helped a little, my fantails now are a mixture of different breeds and I do not inbreed so I constantly buy new birds for the ones I breed. They all have names too

. There is also a pigeon called the Indian fantasy, which is not technically a fantail but the Indians were used in its creation and the pigeon still has a fanned tail so you could check them out too.