Cocoa
From the Apple site: Cocoa is an object-oriented application environment designed specifically for developing Mac OS X-only native applications. The Cocoa frameworks include a complete set of classes, and for developers starting new Mac OS X-only projects, Cocoa provides the fastest way to full-featured, extensible, and maintainable applications. You can bring applications from UNIX and other platforms to Mac OS X quickly by using Cocoa to build state-of-the-art Aqua user interfaces while retaining most existing core code.
More detailed information can be found at http://developer.apple.com/cocoa/
The Predcessor to Cocoa was OpenStep.
Cocoa/GNUstep relationship
Cocoa/GNUstep API Compatiblity map
TBW - to be written - please contribute. What is envisioned for this section is a color-coded compatibility matrix listing all Cocoa API elements, with green for 'should be fully fully compatible', yellow for partially compatible, grey for 'currently incompatible', and red for 'not within the scope of GNUstep/no current or future plans to implement')