Types of electrical wire usually separated in 3 category:
Power cable
control cable
Instrument cable.
You may familiar with some Insulation and Jacket type such as THHN/THWN PVC/NYLON FR-XLP RHW-2 OR RHH OR USE-2 FR-XLP HMWPE, LSZH.
Here are only few cable types and their applications example:
600 V THHN Copper conductor: For use in general wiring application and power in conduit. 600 V RHW-2 Copper Conductor: For use in harsh environments for general wiring direct burial. 300 V UL type PLTC: This is a multi-pair instrumentation cable: For use in instrumentation and process control applications
Copper Electrical Wire Copper is the common used because copper is a very good conductor, and is easy to mold and bend.
Aluminum Electrical Wire Aluminum is cheaper and more abundant than copper. It is also easy to shape and bend. More important for electrical designer is to select the right size of electrical wire . The following link is the method of how to determine cable size.