POSIX and UNIX
The original POSIX 1003.1 was essentially the same as the UNIX System V Interface Definition (SVID), Issue 2 published by AT&T around 1986. This was effectively the definition for System V release 3 (SVR3), although I think that it may have included stuff that appeared in SVR3.2. The last version of the SVID was issue 4, that was updated to conform to one of the slightly later versions of POSIX 1003.1, maintaining compatibility between the core genetic UNIX and POSIX.
I attended the SVR4 Developer conference in around 1988, and as part of the bundle of bumph given out, it included a copy of this issue of the SVID, which is still sitting on a shelf in one of my bookcases. I was told that I would get a copy of Issue 3 sent to me (which was updated for SVR4), but it never arrived.
The SVID (and hence the first edition of POSIX 1003.1) defined more than just the command set. It also defines a mandatory set of system calls, (essentially Chapter 2 in the UNIX manual) but does not describe any of the other sections, like the C library or device types.
POSIX 1003.1 has evolved quite a lot since then, and the various UNIX standards now maintained by The Open Group have taken over the maintenance of the UNIX brand, merging POSIX with the other UNIX branding.
I know why, but it's a shame that Linux as a community (whatever that is) has not bought into the standards promoted by The Open Group, or have not set up a similar single branding standard (forget the Linux Standard Base - it's dead), because variation between different Linux distributions are one of the reason why we see fragmentation of the Linux ecosystem.