Puntius tetrazona, the familiar Tiger Barb

Puntius tetrazona (Tiger Barb). This is the barb that's usually meant when someone just refers to their "Barbs." Tetrazona does mean "four bands," just as you figured; the "zone" is feminine in Latin. 
 
P. tetrazona has a natural range in Sumatra (in the US it used to be known as Barbus sumatranus) and in southern and eastern drainages of Borneo. Mainland populations found in Thailand and Malaya (with a sighting or two in Cambodia) are likely to be escapes of captive fish. So here's another freshwater fish (like some Bettas and Rasboras) with modern surviving populations that got separated when the sea level rose after the last Ice Age, drowning all the low-lying stretches of what the geologists call Sundaland. During the glaciation, though South East Asia remained unglaciated and mild, so much of the earth's water was locked up in vast ice sheets, that the world's sea level dropped by many meters. The South China Sea drained away, exposing its vast flat continental shelf. That area became a gigantic savannah, with stretches of marshland and coastal peat forests linking what are now the islands of Sumatra and Java and Borneo to the Asian mainland. The UCLA Barber lab site offers animated maps that show you the expanded and linked-up river drainages in South-East Asia during the glacial maximums. Imagine the flat endless watery landscape of today's lower Mekong River and its delta, then expand it, if you can, to the scale of the Amazon basin. Starting about 8000 years ago, sea level began rising in fits and starts, and separate "relict" populations of many freshwater fishes became isolated on the large Indonesian islands. If this is interesting to you, you might like to see an article describing how populations of Arctic char got stranded in Ireland, becoming purely freshwater fishes, as the Glacial Age ended, at the Irish Char Conservation Group website.
 
In the wild, Tiger Barbs inhabit both clear and turbid shallow waters with a moderate rate of flow. In the 1980s wild P. tetrazona were collected from swampy Malayan lakes with changable water levels and unexpectedly high carbonate levels. In captivity, optimal growth is at 72º-78°F, with breeding at 75º-82°F, the U.S. Department of Agriculture found, in the interesting document on techniques for breeding and raising Tiger Barbs from Hawaii's Center for Tropical and Sub-Tropical Aquaculture. The document was developed to help the nascent Hawaiian fish-farming industry, but its information will be interesting to you, too. Tiger Barbs get a bad rap for fin-nipping and chasing slower fish, especially slow-moving ones with long-flowing fins like Gouramis. Keep them in a school, that's the first thing you'll hear about them. The fact is, Tiger Barbs form more of a pack than a school. Within the group there's lots of competition, which isn't limited to the males. As long as you have 8 or 9 Tiger Barbs together, they're completely occupied with keeping up their own standing with the others. A solo Tiger Barb, lonely and bored, looks for some stimulating mutual harassment, and the trouble starts. So keep your Tiger Barbs in a swarm.
 
A stepped-up regimen of water changes will effect a change in these fishes: snouts glow cherry red, the males sport brilliant red in their fins, and silver scales take on golden tones. As Tiger Barbs age, more melanin gets deposited in their skin. Scales develop black edges that give them a netted look, and in certain lights their black markings iridesce with a green shimmer. This is called the Tyndall effect, from the physicist who first described how it works, and it results from scattering of shorter lightwaves— the blue light— by finely-scattered reflective particles that lie in the outer skin, above the dark layers of melanin pigment deeper in the dermis.
 
Selected color varieties of Puntius tetrazonus are on the market. These are not a separate species, or hybrids of Puntius tetrazona with another barb: they are mutations, in fact. There's an albino mutation— isn't there always an albino version?— which in the late 1990s began to be dipped in dyes in the Singapore fish mills to invent a spurious kind of "lavender barb." Aagh! Don't encourage this low practice by purchasing such tainted fishes. But a beautiful natural selection is the Mossy Green Barb that was developed by Singapore breeders. Here for once is a domesticated selection that has a natural look, in which the fish produce so much extra melanin that the black bands have joined up. In a good example— the only kind you should buy— there isn't even a "saddle" of silver on the back; only the belly remains silver, and the snout, which darkens to cherry red when the fish are in glowing health. And as a result of the Tyndall effect I was telling you about, the black areas glisten with a strong green iridescence. These fishes are spectacular displayed with well-conditioned Puntius nigrofasciatus.
 
Links. Puntius tetrazona at SeriouslyFish.
 
Puntius tetrazona at FishBase. Puntius tetrazona at Wikipedia.