There are also some flies that can be fished both dry and wet. These are usually things that are meant to mimic a nymph (an immature bug).
Dry flies are considered the most pure form of the sport, and are generally used primarily for trout. They imitate bugs almost exclusively (they can imitate a mouse or frog, and some other things, but usually bugs), and are used for trout most of the time. Some notable exceptions are hoppers and beetles, which are used for bass and panfish as well. Wet flies are used for a wide variety of species and include flies that imitate bugs, baitfish, crabs, crayfish, and a bunch of other stuff. Streamers are a separate distinct type of wet fly that's intended to imitate baitfish. Poppers are large surface flies that generally are made of floam or deer hair and create a lot of commotion on the surface. They are technically a dry fly, but are really in their own category. They sometimes are designed to dive under the surface a little when they're stripped in hard. Streamers and poppers are used a lot for saltwater fishing, as well as a few other things like clousers, gotchas, crab, crayfish, and lots more.
I hope this isn't too much info!