A header-back exhaust replaces everything from the tips of your exhaust all the way to the header. These types of aftermarket exhaust packages are by far the most expensive, but also offer the best power gains and sound improvements, and improve your engine breathing the most as they increase the overall diameter of your entire system.
A cat-back exhaust system replaces everything from the back to the catalytic converter. This means that these typically come with an included muffler and a tailpipe, but can also sometimes come with a mid-X/H/Y pipe as well. Cat-back systems are the most popular ones on the market because they are the best bang for your buck while also improving the sound and the engine output considerably, but not as much as a header-back system.
Finally, we come to axle-back exhaust systems which replace everything from the back to the rear axle. An axle-back system is the cheapest and easiest one to install, but it does not sound as good as the other two, and it does not improve your power output as well as a cat-back system, let alone a header-back system.
A single exhaust configuration is the more common setup and features a singular set of exhaust components from the engine to the very tip. These tend to offer the best power gains as they usually offer the widest diameter pipes with the least amount of flow restrictions.
A dual exhaust configuration is the same as a single configuration in regards to the headpipe, the converter, and the muffler, but comes with dual exhaust tips exiting the muffler. These don’t offer nearly the same power but are loved because of how they look.
A steel exhaust is the cheapest one on the market but also tends to rust after a while. As such, going for a stainless steel exhaust is the better option.
Inconel and titanium exhaust pipes are lighter and they resonate better than steel exhausts. Moreover, they are also more durable because they do not corrode. However, these are still relatively rare and they cost a lot more money than any form of steel.