Mufflers muffle the sound of the exhaust system. They are typically the final part of the exhaust.
Resonators are basically a pre-muffler. They are usually straight-through in design and remove the rasp from an exhaust system.
The catalytic converter is a device used to reduce the toxicity of emissions from an internal combustion engine.
Each bank of cylinders has a header, which combines each exhaust port from the cylinder head into one pipe.