The Veil Tail

White veil tail betta

The most widely-available longfin form in bettas is unarguably the Veil Tail betta (or VT). This is the natural form the fins take when they are artificially lengthened from the wild shortfin form with selective breeding. This is the type of finnage usually seen in Pet Stores. Though attractive in its own right, it is generally considered undesirable among those breeding for show-quality form. In fact, the IBC (International Betta Congress) doesn't even have classes for Veil Tails any longer, and it has become a sentiment of negativity to describe any high-bred betta of 'going veil-ish'.

The Veil Tail betta has a caudal that tends to arch and then slope downward, like a wedding veil. 

Link