What is the difference between a supersonic plane and a non-supersonic plane?

As far as I can tell there are three main differences aside from the fact planes that fly faster than sound are faster and more powerful.

1. Supersonic planes have fully moving tailplanes. This is also known as a an all flying tailplane. In flying faster than sound shock waves from the leading edge make the conventional tail functionally useless.

2. Air going into the jet engine needs to be slowed down so the engine is not destroyed. This is hard to do because you want to slow down the air enough. Most jets have ducts that move to slow the air depending on the speed of the aircraft.

3.When flying faster than sound the center of lift of the wing will change location. As a result the center of gravity needs to be changed in some way to balance the aircraft. Some planes have used movable weights to take care of this.