Yes, just two types: copper wire, often tinned to minimise corrosion; or graphite, sometimes referred to as carbon. Carbon is a bit of a generalisation as it comes in several forms, e.g. diamond is a form of carbon. But graphite is the only form of carbon that will conduct electricity, so that is a more fitting name for the plug leads. It is also good at withstanding heat..
The reason for graphite over copper is to introduce some electrical resistance to quench some of the spark energy, in order to reduce radio frequency interference. That can have a marked effect on electrical equipment in the car and also on domestic tv and radio reception. If you cut one open, the core looks like a slippery black, stringy material. It is in fact fibre glass impregnated with graphite powder.