Building for Mac App Store; Release or Distribution?

If you are referring to the build configuration, probably Distribution. I assume that it must be signed, and if you follow the signing tutorial on Apple, you will likely name the build configuration Distribution.

 

Mac projects usually have either a "Distribution" or a "Release" build configuration (along with "Development" or "Debug", respectively), depending on when you started with the then-current project prototype. They're pretty much the same thing, though; Apple simply made the configurations' names more straightforward at some point.

That's why personally, I've never seen a Mac project that had both a "Distribution" (older name) and a "Release" (newer name) configuration. If you do have both of them for some reason, either of them should work fine for submitting to the Mac App Store.

As far as implementing differences between your own distribution (e.g., use Sparkle, check your own licenses/serials) and the App Store build (e.g., check App Store receipts, adhere to App Store requirements) is concerned, I'd recommend doing that in separate targets, as opposed to a third build configuration, because then you can actually work with different sets of frameworks, for instance.