What is a muscle car

Everything I read said the origin of the term "Pony Car" is named after the Ford Mustang, the first car of this type... is this correct?

Well, the First Mustang, and the First Barracuda were both released in 1964.

Yes, the Mustang is THE pony car. So is the Barracuda and the Camaro, in '67. The were the "Trans Am Racers" of the day, there were others too, The Cougar, and there was an AMC entry, too.