Display Postscript in NeXTSTEP was replaced with Quartz in OS X and iOS. DP has licensing issues with Adobe, and I believe there were performance issues with the client/server architecture of DP that were resolved with Quartz.

The NeXTSTEP "Workspace" and file manger were replaced with Finder in OS X. Finder was a direct port of the classic Mac OS Finder, implemented in C/C++ using the gnarly but powerful Carbon file manager APIs rather than Objective-C, Cocoa, and the comparatively limited NSFileManager APIs (limited icon support, no file alias support, no asynchronous or interactive file operations, etc.)

The Carbon Hot Key APIs came from Classic Mac OS and are still the only way to do global hot keys in OS X. They're one of the few bits of Carbon still supported in 64-bit OS X.