I THINK they're called "Plakat Bettas".... I found a site that listed quite a few different Betta tail types and there was a picture of a male betta with the exact same fins (dif. color) but it said he was a Plakat Male. Apparently these are the kind that are found in the wild and the short fins allow for them to move around quickly without weighing them down. You could google "plakat bettas" and see if the pictures match the fins of your betta!
Here are some updated photos of her in more "natural" surrounding - she's beautiful and she rules the tank! Our other 2 females keep their distance! lol
On a sad note both our males died in the last week. Sumo our splendens died from old age and Chaing was found wedged between 2 rocks that had collapsed on top of him! I think he was chasing the live bloodworms I fed them that night and disturbed the rocks...
The last photo is 1 of the 2 surviving fry from Chaing's first attempt. I thought he had eaten them all but found the 2 hiding under the driftwood when I replaced the gravel in his old tank!