The Venus Fly Trap, or Dionaea muscipula, is part of a monotypic genus, meaning that there is only one species in the genus Dionaea and that species is muscipula. Unlike other plants, it isn't possible to grow different species of the genus that have distinct traits. However, through cultivation and some harvesting of unique plants from the field, there have been multiple cultivated varieties, abbreviated as cultivars, of Venus Fly Traps established that have certain characteristics that make them distinguishable from a typical Venus Fly Trap.
A cultivar can be a plant or a very similar set of plants that have characteristics that make the plant stand out from other plants of the same species. You can think of cultivars like breeds of dogs. Just like certain breeds of dogs have defining characteristics, but they are all from the same species, it is the same with cultivated varieties of Venus Fly Traps.
So how do cultivars come to be? Well, it is actually a quite simple process. The description of the cultivar must be published in a widely published journal or book and the author of the cultivar description must register with an "International Cultivar Registration Authority" (ICRA). The ICRA for carnivorous plants is the International Carnivorous Plant Society. You can find the registration forms on the ICPS website and you can also submit a description to the ICPS newsletter for publication if you have a particular plant that you would like to make an official cultivated variety.
It is important to notice how cultivar names are written. You can identify a cultivar name by the fact that it is enclosed in single quotes. Double quotes indicate a descriptive name, but not an official cultivar. For example: D. muscipula 'Red Piranha' is an official cultivar name and it is put in singled quotes. However, D. muscipula "All Red Giant" is just a descriptive name for a particular plant that isn't an officially registered cultivar.
The preferred method to propagate most Dionaea muscipula cultivars is vegetatively. Because vegetative propagation results in plants that are genetically identical to the parent plant, this is the simplest way to ensure that the genetic integrity of the cultivar is retained. However, it is possible to propagate cultivars sexually from seed provided that the offspring do in fact retain the characteristics as they are described in the cultivar registration. This is why it is important to have a very good description of a cultivar so that it is possible to be sure that the seed-grown offspring do exhibit the exact characteristics required to be considered the same cultivar as the parent plant.
Venus Fly Trap Cultivars
I have created a comprehensive list of all registered Venus Fly Trap cultivars. The International Carnivorous Plant Society has a list here, and the most current listing of Dionaea muscipula cultivars is kept in the Carnivorous Plant Database here, and as of February 16, 2009, they are both up to date.
To see as good of a list of Venus flytrap cultivars as I can find on the web, be sure to see my list of Venus Fly Trap cultivated varieties.