There's some confusion and different marketing terms out there. RAID 6 is a common one. RAID 6 is an extension...
of RAID 5. RAID 5 is some number of disk drives, we'll call it N + 1. N could be five drives plus a parity. Six total drives, five actual data drives. The drives are striped with parity interleaved to optimize performance.
RAID 6 adds a second parity drive. So, think of it as N + 2. Seven total drives. The need for RAID 6 is larger drives. It takes longer to rebuild larger drives when a drive fails, so you have a longer exposure window if something happens. Having that second parity drive protects you from an additional drive failure during the rebuild. That's the basic idea behind dual parity.
With distributed parity, the parity may be distributed onto another array. One way to do that is with two arrays clustered together where the data is actually replicated across different storage systems. It may not be parity protection, per se, but it is a form of protection. There are some other techniques that involve spreading parity bits across different storage systems and across wider areas. We're starting to see some companies, such as Cleversafe, in the wide area distributed game, where the data and parity is spread across different locations.
Check out the entire RAID FAQ guide.