What is the DARWIN IOS?

Darwin is the background Unix environment behind all of Apple's OSes newer than the Classic operating system.

The Classic operating system refers to the operating system available for Macs from 1984-2001.

iOS - the operating system behind iPhones, iPod Touch, and IPads.

Mac OS X - name for the Mac operating system starting in 2001. Classic operating systems could run along side Mac OS X on Macs till early 2006, and as a boot system until 2003 in new Macs.

Mac OS X 10.5 ended the ability to do Classic along side Mac OS X, but still allowed booting of Classic operating systems separately from Mac OS X on those Macs that supported it from 2003 and earlier.

Starting with Sierra 10.12, Apple started naming Mac OS X, Mac OS again. Talk about confusing, but that's what has happened.