In times when disk drives were optional rather than default features of operating systems, being a disk operating system (i.e. disk-based or disk-aware) was a mark of superiority.
A number of such systems exist; the Commodore 64 home computer had a DOS, as did (on the other end of the spectrum) IBM's System 370 and System 390 series of mainframes (DOS/VSE, Disk Operating System/Virtual Storage Extended).
The most popular family of operating systems called "DOS" is that running on IBM PCs. The original version was provided to IBM by Microsoft, and marketed as "PC-DOS". Later versions were also sold as "MS-DOS". Digital Research produced a compatible variant known as "DR-DOS", and (after a buyout) "OpenDOS". There is also a free version named "FreeDOS".