Electrical wire comes in nearly all sizes and shapes (it's flexible), but for the most part, you'll find it copper which is a great conductor, aluminum
which is not such a great conductor, and copper clad aluminum which is a combination of both copper and aluminum, with conductivity properties somewhere in between.
The most common type of wire that electricians use is RX otherwise known as Romex.
This type of wire is used indoors and comes in various sizes and types. For instance, 14/2 RX is rated at 15 Amps and has two insulated conductors plus an uninsulated ground.
12/3 RX is rated at 20 Amps and comes with three insulated conductors and an uninsulated ground conductor.
10/3 Rx is rated at 30 Amps, and 8/3 is rated at 40 Amps. The NEC provides various tables specifying wire uses and ratings.
Another type of wire is UF which is very similar to RX except that it is rated specifically for Outdoor - Underground use.
MC wire has a metal jacket on the outside and is used in many of the same areas as RX. It is used where extra protection is needed (hence the metal outer jacket) and very often in commercial installation.
THHN wire are individually insulated stranded conductors, and must be sleaved within some type of protective conduit. They also vary in sizes, and as with the other types of wire mentioned, are copper conductors.
The main difference is the fact that RX, UF, and MC all have solid conductors instead of stranded. Because of this fact,THHN is obviously easier to pull through conduit.