The most common worms for composting (in North America) are Eisenia fetida, otherwise known as red wigglers.
It is extremely important that you use only surface worms, or epigeic worms (also called manure worms) for composting. The common earthworm, Lumbricus terrestris, is not a surface worm; it is a deep burrower, an anecic worm. Anecic worms build permanant borrows. Not only will they not do the job, they are likely to die in a bin.
True fact! Earthworms such as Lumbricus terrestris and Eisenia fetida are not native to North America, and are considered an invasive species. They are currently and actively decimating many US northern and Midwestern forests, because well-meaning fishermen "return" unused worms to the wild (they "dump out the can" after a day's fishing).
Adding to the problem, a lot companies now sell worms to gardeners. Not only are the worms likely to just crawl off if the environment isn't to their liking (a likely scenario if a gardener purchased worms to try and improve the soil in the first place), they reproduce like crazy.
Even so, Eisensia fetida and Lumbricus terrestris are both long and well-established species on the North American continent. They established a foothold (so to speak) in North America almost as soon as Europeans began settling here. They were introduced accidently, via ship ballast and tangled up in the roots of plants.
So, what's a conscientious worm farmer to do? Never release your worms into the "wild". Even if your environment is urban, don't release your worms. In the ground, worms are the megafauna- the "whales" in their ocean of soil. They are far larger than almost any creature under there; fungi, springtails, bacteria, nematodes, arthropods. They quickly overtake a biosphere and can radically change it. If you have to get rid of your worms, donate them to a school or give them to a community garden, where they will be welcomed.