Uhmmm - barkmonster is correct. There is only one real Unix and it was developed at AT&T. The important of Unix was to write an operating system in a coherent language (C), have a consistent API, and set of commands. The folks Berkeley didn't want to pay AT&T a royalty, so they essentially reverse engineered Unix and produced BSD, which had the same APIs, command line interface, written in C, etc. but was royalty-free (and source code was available). Unix (and later Posix) has evolved into a set of specifications,
http://en.wikipedia.org/wiki/Single_UNIX_Specification, for implementing an operating system that can be called Unix. Mac OSX is based on Darwin,
http://en.wikipedia.org/wiki/Darwin_(operating_system), which uses code and ideas from a variety of Unix operating systems, such as BSD, Mach, etc.
I believe what barkmonster means by "Unix variant" is Unix-like,
http://en.wikipedia.org/wiki/Unix-like, which include Unix, OSX, Linux, BSD, etc. All of these are operating systems,
http://en.wikipedia.org/wiki/Operating_system, and not applications. However, the line gets blurred with virtual machine technology,
http://en.wikipedia.org/wiki/Virtual_machine, where you could argue that an operating system running as a VM is actually an application in the strict sense.
I would recommend that lordthistle do a little research...