What is POSIX
The Short Answer
Today, POSIX is the same thing as the Single UNIX Specification Version 3 or ISO/IEC 9945:2002. This is available from http://www.opengroup.org/onlinepubs/007904975/toc.htm
Some History
Once upon a time, the Single UNIX specification and the POSIX Standards were separate entities. The Single UNIX specification was released by the "Open Group", and was freely available as per their requirements. The latest version is The Single Unix Specification Version 3.
The IEEE POSIX standards were released as IEEE Std 1003.[insert various years, revisions here], and were not freely available. The latest version is IEEE 1003.1-2001 and is eqivilent to the Single Unix Specification Version 3.
The two separate standards were merged into what is known as the Single UNIX Specification Version 3, which is also standardised by the ISO under ISO/IEC 9945:2002. This happened early in 2002 or so.
The Standard
For a good overview of the different parts of the standard, see http://www.unix.org/version3/overview.html
