The exhaust manifold is attached to the car's engine. To be specific, it's connected to all your engine's cylinders, where it'll collect exhaust gases and channel them into a single exhaust pipe. Usually, the manifold is made of cast iron and is designed to take up the least amount of space possible.
For better performance, it's possible to get an aftermarket header and replace the stock manifold that came with the car. This is often done to increase the car's power output. If you are looking for the best exhaust system parts, then you can find the best performance parts by searching online.
Further down the exhaust system is the catalytic converter. The reason it's called a 'converter' is that it converts dangerous emissions to water and carbon dioxide. The converted emissions include carbon monoxide, hydrocarbons, and nitrous oxides.
The exhaust system's piping isn't just the part that sticks out the back of the car (which is called the tailpipe, by the way). There's actually a fair bit of piping that goes into the car and connects all exhaust components. Not all piping is made the same, especially when it comes to automotive exhaust systems.
Some exhaust systems will also have a resonator. This will either be as part of the muffler or as a separate component. Resonators serve the same purpose as a muffler, which is why these two parts complement each other.
Where a muffler allows sound waves to bounce off its internal walls, resonators are actually wider sections of piping. Because of that extra width, sound waves bounce around inside the resonator and cancel each other out.