Betta tails can be roughly classified into several different basic forms.
Bettas with veil tails are the most common form seen in pet shops, and the most frowned-upon form for high-quality betta showing and breeding. Veil tail bettas have caudal fins that arch and then flow behind the fish, looking like a wedding veil.
Double tailed bettas do not actually have two tails. Rather, they have an additional dorsal fin that is equal in length to the anal fin, creating the illusion of two tails or a lobed tail. The mutation is desirable for aesthetic purposes, but breeders must be careful when selecting double-tail bettas for breeding stock, because they often have spinal deformities or partial paralysis.
Pronounced pluh-COT, the Plakat tail betta is the oldest and most natural form of the species. Plakat tail bettas are not popular for aquarists seeking flashy ornamental fish, but betta enthusiasts enjoy them because they--like their wild ancestors--are active, stout, and healthy.
Some betta strains have a unique and gorgeous appearance, caused by a mutation that reduces the webbing between fin rays. The result is a tail that looks spiked, as if it has prongs. The deeper the reduction of webbing is, the better, when it comes to show-quality crown tail bettas. Coloration that complements the mutation is especially attractive.
A close relative of the crown tail, comb tail bettas have a similar reduction in the webbing between fin rays. However, the webbing is not reduced to the same extremity as crown-tails, and the visual effect is a slightly spikey appearance rather than a deeply pronged appearance.
Single-tail bettas, also called round tails, have neat, single tails with rounded edges. Although often confused with the delta tail (see below) they are in fact a different classification. An ideal round-tail betta has a nearly circular anal fin.
A delta-tail betta looks similar to a round tail betta, but its tail fin extends further up, as to nearly touch its caudal and dorsal fins. Although the tail does not arch straight up (as in the halfmoon tail betta), it extends upward in a fan-like shape. Bettas with extreme delta tails that are not quite wide enough to be classified as half-moons are called super deltas.
Half Moon Tail
A spectacular sight to behold and a popular attraction at betta shows, the enviable half-moon tail betta has a large tail that extends fully upward and outward, to create a full 180-degree semicircle. The tail makes a complete "D" shape that runs perpendicular to the betta's spine and is symmetrical on all sides.
Selective breeding of the halfmoon tail betta has created a unique strain called the rose tail, which looks like the half moon tailed betta, but with extreme overlapping of all three fins. The angles of the rose tail betta's wide anal fin are so broad that it actually overlaps the caudal and dorsal fin. This mutation is beautiful, but carries some drawbacks, and individuals with the trait have difficulty swimming and often spawn sickly or deformed fry.
Spade tail bettas, as the name suggests, have simple, single, rounded tails with pointed ends. Although once a very popular breed--even outselling the veil tail in some areas--it is now somewhat obscure and has fallen out of popularity in home aquaria.