It's hard to top a response like winnie's.

Just one other comment on the size of wire to it's current carrying capacity. Think of it in terms of not how much current a wire can carry, but how hot it gets while carrying it.

You'll notice in the ampacity spec pages that there are various ampacities listed for different types of insulated wires, yet they have the same guage. It is a question of how hot that wire will get before its particular type of insulation melts. So while THHN insulated 12 AWG wire is limited to 20 amps, this same conductor can carry significantly more than that if it is asbestos covered.

When you get to your transformer, gauging the wire will not tell you how thick the insulating varnish is, or how well air can circulate around them. It's all about heat disipation.

Large power bank oil filled transformers often have several ratings, depending on how they are cooled. For instance, you might see a transformer rated at 12/16/20 MVA OA/FA/FA. This would translate to 12 MVA in open air (OA), 16 MVA with one bank of fans running (forced air or FA), or 20 MVA with both banks of fans running (FA?FA).