POSIX itself is a set of standards which define the APIs but isn’t itself an implementation
POSIX is a standard, or rather a whole series of standards. It also covers things like the shell and shell utilities, and the semantics of various kernel services, as well as the C libraries. These days you might want to look up SUS (Single Unix Specification) too.
https://en.wikipedia.org/wiki/Single_UNIX_Specification
https://en.wikipedia.org/wiki/POSIX
POSIX specifies the API available to programs, and also shell and commands and stuff available to users. It does not specify which functions should be available from the standard C library, and which should be available from the kernel: from the standpoint of POSIX, it's all the same. POSIX doesn't care how the API is implemented, just that it is implemented correctly.
It's more or less a standard that describes how UNIX compatible OSes are supposed to work. That includes the APIs/ABIs as well.
At least that is how I understand it.