ZDP stands for "Zero Day Package", sometimes redundantly called a "ZDP Package". However, this is not using the term Zero Day in the security vulnerability sense. Rather, it's referring to day number zero: The first day the product is available to the public. The Zero Day Package is a Windows Update package that is made available on launch day. These patches are reserved for addressing serious functionality issues in important scenarios. For example, if there's a fix for a crash in a commonly-used scenario, that's a candidate for a Zero Day Package.
Note, however, that even though the package is available on Day Zero, it won't be installed on Day Zero. Windows Update will download the package and stage it for installation, but it won't install it right away. It'll wait a few days (I forget exactly how many) before starting to encourage you to update. The theory is that you get a few days of playing around with the new system before you start getting nagged about updates.
This artificial delay before installing the ZDP means that the official release version of Windows needs to be solid enough to survive a week without any help. If you have a problem that is super-critical that cannot wait a week, then you need to get your fix into the OOBE ZDP.
OOBE (pronounced /oo-bee/) stands for "Out of Box Experience". It's the program that runs when you turn the computer on for the very first time after you take it out of the box. OOBE doesn't have the luxury of taking a fix in a ZDP, because by the time the user signs in and installs the ZDP, it's too late. OOBE is already over! OOBE needs to run right the first time. No second chances, no patches.
Okay, back to the OOBE ZDP. The term OOBE ZDP does not mean "The ZDP to fix OOBE bugs." Rather, it means "The ZDP that is installed by OOBE."
The OOBE ZDP is a special ZDP that is downloaded and installed at the end of OOBE, part of the "Please wait while we apply the finishing touches" phase. Since the user is sitting there waiting anxiously to start using the computer they just got for Christmas, the OOBE ZDP needs to be small, so only the most critical fixes go there.
Update: See corrections from Michael Ratanapintha below. Thanks, Michael!