The man page does give some definitions:
The following operand shall be supported:
pid One of the following:
1. The unsigned decimal integer process ID of a command, for
which the utility is to wait for the termination.
2. A job control job ID (see the Base Definitions volume of
IEEE Std 1003.1-2001, Section 3.203, Job Control Job ID)
that identifies a background process group to be waited for.
The job control job ID notation is applicable only for invo-
cations of wait in the current shell execution environment;
see Shell Execution Environment . The exit status of wait
shall be determined by the last command in the pipeline.
The job control job ID type of pid is only available on
systems supporting the User Portability Utilities option.
So basically, it's looking for one or the other, process number or job ID. In Linux, we typically refer to that unsigned decimal process number as the pid. Since this is a POSIX man page, it's set up to be able to apply to a number of different operating systems (Linux is not 100% compliant), so the job ID probably doesn't apply to you. I'd quit worrying about it, and just understand that every time they say job ID, that means pid to you.