What is the difference between distributed parity and double (dual) distributed parity in RAID?

Distributed parity is RAID5, the parity data are distributed between the physical disks and there is only one parity block per disk, this provide protection against one physical disk failure, the minimum number of disks are3.

Dual distributed parity is RAID6, the parity data are distrubuted between the physical disks and there are two parity blocks per disk, this provide protection against two physical disks failure, the minimum number of disks are4.  

Basm Allah Alrahman Alrahim

Parity used with error detection and correction at Communication and computer systems , it has a lot of techniques

you asked that question because of RAID5 and RAID6 I think

RAID6 = Extend RAID5 ( RAID5 with2 Blocks for Parity )

There is a  Copmarison Between All RAID Level at this Link in English and This Link For Arabic