On the R18 when you open the hood you will be looking at a large semi round silver/gray heat shield. That is your catalytic convertor. Its bolted right to the "exhaust manifold" port on the block. The exhaust manifold is cast into the block and just has one large (relatively) opening. From the catalytic convertor there is a small "down pipe" if you can call it that. That short section connects the cat to the mid pipe of the exhaust. The mid pipe runs basically the full length of the car back to the muffler.
On these cars there really isn't a header. People call it that for ease of terminology. Replacing the cat is where you would put a "header" but most of them are just a "test pipe" as they call it. That will bolt in place of the cat and connect to the "down pipe." I know there are companies that offer that short section and call it a down pipe buts its really not a DP in the sense of the ones you see for the Si.
In this diagram you see the cat which is bolted to the block: The big round cylinder. The
E-10-10 tag is where it bolts to the block and you see the single opening. At the bottom notice the
B-2 tag.
This is the rest of the exhaust setup: Notice on the left front of the image the small kinked pipe with the
E-4 tag. That is your "down pipe" which bolts to the
B-2 on the above image. Then the long mid pipe and finally follow the zig-zag to the muffler. This part is referred to as the axle-back section. So if you see an axle back for sale its just that last piece. A catback system will replace everything from the mid pipe back. Usually those exhausts do not replace that small "down pipe" section.
Hopefully that helps you understand what each piece should be and might be called when shopping.