MS-DOS (and the IBM PC-DOS which was licensed therefrom), and its predecessor, QDOS, was a successor to CP/M (Control Program / (for) Microcomputers)—which was the dominant operating system for 8-bit Intel 8080 and ZilogZ80 based microcomputers.
Early versions of Microsoft Windows were programs which ran under DOS. Later versions were launched under DOS but "extended" it by going into protected mode. Still later versions of MS Windows ran independently of DOS but included much of the old code such that it could run in virtual machines under the new OS and the latest versions of MS Windows are continually dropping ever more of the DOS ancestry.
Under Linux it's possible to run copies of DOS and many of its clones under dosemu (a Linux native virtual machine program for running real mode programs). There are a number of other emulators for running DOS under various versions of UNIX, even on non-x86 platforms.
Prior to (and to some extent concurrently) the development of the IBM PC compatible family of microcomputers, several other operating systems for other architectures were already known as DOS, notably:
The DOS initial/simple operating system for the IBMSystem/360 family of mainframe computers (it later became DOS/VSE, and was eventually just called VSE).
The DOS operating system for DECPDP-11minicomputers (this OS and the computers it ran on were nearly obsolete by the time PCs became common, with various descendents and other replacements).
The DOS operating system for the Apple Computer's Apple II family of computers. This was the primary operating system for this family from 1979 with the introduction of the Disk ][ floppy disk drive until 1983 with the introduction of ProDOS.