From my understanding, I believe there are two different types of hoods. There is one without a mask, and one with a mask. Maskless is the one you get when you join the Brotherhood, and the Masked version you need to find. I believe you can find it through the Dark Brotherhood quest.
Yes, and they have different stats, maskless gives stealth bonus, with mask gives archery-bonus, 20% better sneak or 20% more damage.