For Windows there is Win32 API, what about for Mac? On Wikipedia
http://en.wikipedia.org/wiki/Cocoa_(API)
it is said that Cocoa is "one of" the API... what about the full story?
At what level? The low level API is largely but not entirely FreeBSD, and below that there is still a Mach API (some things still use Mach ports for IPC, I believe; at least, launchd supports them). At the upper level are two APIs: Cocoa and Carbon. Cocoa is the native API; Carbon is intended for programs ported from older MacOS. (Which includes parts of OSX itself; for a long time Finder was a Carbon app.)
The Windows situation isn't all that different, actually; there was for a long time a Win16 emulation API present in 32-bit Windows, and in the early days of Windows NT it had both POSIX and 16-bit OS/2 APIs.