Both of the Betta's in your pictures, "me" are perfectly healthy. That is just how the Delta tail Betta's fins are.
There are so many different types of Bettas that yours could just have short fins. If you happen to see any shredding, tearing or white tipped fins, I would suspect fin-rot. If there is none of this, then be happy with it!
EDIT: Andy, now..This is a Betta with fin-rot:
http://www.bettatalk.com/images/fin_and_tail_rot_copy.gif
Obviously you can see that there is a darkening mucus at the tips of the fins.
This, is a Crown tail Betta that is perfectly healthy, just like both in "me"s post.
http://www.theaquariumwiki.com/Image:CT_Black_Orchid_M_betta-1874.jpg
It's normal for certain species of Betta to have oddly shaped fins.
Do you see now?