The Classic environment is Mac OS 9 operating system running as a stand-alone application (a shell) within the control of Mac OS X. Classic applications are Mac OS 9 applications running in the Classic environment. When a Classic application window is in the forefront the Classic environment is apparent by the appearance of the Mac OS 9 menu system. If a Classic application crashes, it may bring down (in classic fashion) the Classic environment, but Mac OS X will continue running. Microsoft Word 98 is an example of an Classic application.
Carbon
Carbon applications are updated Mac OS 9 applications and run natively in Mac OS X. They benefit from UNIX's advanced features such as protected memory and multitasking as well as the look-and-feel of Aqua . Stata 7 and Carbon R are examples of a Carbon applications.
Cocoa
Cocoa applications are Mac OS X applications written with Apple's Cocoa programming framework. They benefit from the UNIX advanced features and the Aqua interface. TeXShop and R Cocoa are examples of applications written using Cocoa.
Darwin
Darwin is the UNIX environment running under the hood of Mac OS X. It is based on BSD 4.4 and FreeBSD 3.2. The GNU 3.1 compilers come with the system. Open source packages are easily compilable or are available precompiled from the distributors or can be managed through the Fink package management system. Shells into Darwin can be started using the /Applications/Utilities/Terminal application. XFree86 (X-Windows) and Apache are examples of Darwin applications.