It's a heavily modified version of the old 4.4BSDLite. So yes, a version of Unix.
Cisco's original IOS is based on the VMS that originally ran on the DEC PDP11/05 at Stanford University. That's where all of the original Cisco founders came from.
VMS still survives as OpenVMS and has a shell very much like any Unix system. Cisco limits your access with a very restrictive shell that only processes certain commands.