First, a word of caution:
Your typical consumer-level motherboard that "supports RAID" uses either their own proprietary software RAID (which limits the OS you can use, usually only Windows) or a "hybrid" approach that uses proprietary software plus some dedicated hardware (but still not a full RAID controller).
So in answer to your question: No, "supports RAID" does not necessarily mean that it has a RAID controller.
Also, you've cited a range of chipsets, not motherboards -- what the chipset supports is a lot less relevant than what the actual motherboard supports, and in fact the chipset supporting RAID isn't really relevant at all -- motherboard manufacturers can (and have been for years) putting RAID (see first paragraph) on their motherboards without the core chipset having its own support for it at all.
And to answer your second question: Nothing special is needed in the hard drive in order to be used in a RAID (unless for some reason the RAID controller/software requires something extra, or doesn't support certain types/capacities of hard drives).
If you're looking to build a server on the cheap, my recommendation is to skip RAID on the motherboard entirely (unless you're going to spring for a full RAID controller -- not cheap, but you can't beat the performance from these beasts!) and then use a software RAID solution; I have 2 Linux servers at home (one a high-capacity file server, one a high-performance VM host) that both use
md for their software RAID, and it works superbly! Plus, the price tag (free) is a heckuva lot cheaper than anything you could find in the hardware market, and if the system fails for any reason (such as the motherboard I'm in the process of replacing on the file server) you're free to get just about any hardware you like -- the software, not the hardware, is responsible for your RAID array, so you cannot find yourself in the pickle of needing to replace a hardware RAID controller that's no longer in production (a situation that more than likely will cost you all of your data!).