Wire has two parts: Conductor and insulation.
Conductor:
Typically copper. Other materials are used for specialty wires.
The conductor can be a single strand or multiple strands grouped together. Trade offs on cost and flexibility. Single strand or solid wire is easier to make cheaper. Most house and building wiring is solid, once in place doesn't need to be flexed. Wire with more and finer strands is more flexible. Battery and welding cables tended to be fine stranded wires. Typical wire used for appliances, equipment and vehicles are a medium stranding.
The size (or gauge) is measurement of the amount of copper in the strand. This size determines the how much current the wire can safety carry. Solid or stranded wires or the same gauge have basically the same amount of copper and same current rating. The current rating for a specific wire gauge comes from a variety of codes and standards based on use: building (residential, commercial), industrial equipment, appliances, vehicles, power distribution, etc.
Insulation
The insulation is the stuff around the conductor that keeps the current flowing in the wire and not to places you don't want it.
The type code (THHN, etc) defines the insulation material on the wire. Some types (THHN, MTW, GPT) are single conductor wires. Other types (NMC, SOOW) are multi-conductor cables (multiple wires grouped together).
The insulation type will define where it can be used (per the code) and wire properties.
- Wet or dry locations.
- Resistance to solvents and greases.
- Exposed or protected/ encased.
- Abrasion resistance.
- Thickness and flexibility.
- Maximum voltage the wire can be used for.
- Temperature rating.
THHN is used in a lot of building wiring and is commonly available.
There are a multiple wire types used in automotive wiring including GXL, SXL, GPT, SGX, etc.
I have done industrial equipment and control system design for 30 years and have specified and used a lot of wire.