Practically if not actually every single UNIX-like operating system today makes the distinction between multi-user and single-user modes. Single user mode is generally intended for low-level system maintenance which cannot be performed while the system is up and running normally, even with a reduced set of services (often file system maintenance that generally needs to be done offline).
However, someone obviously had to write the first code to actually distinguish single-user mode from multi-user mode.
I suspect that multi-user mode came after single-user mode, simply because multi-user mode does more things and it makes sense to start the system initially in single-user mode and only later transition to multi-user mode (and that is how at least Linux does it; the kernel works in "single user" mode as evidenced if you pass e.g.
init=/bin/bash to it, and then effectively
init switches into multi-user mode), but my question is: when, and which variant/version, was the distinction between the two first made?