MS-DOS refers to "Microsoft DOS", the Microsoft-developed variant of DOS. Because of the prominence of Microsoft in computer industry, it is frequently the case that people refer to "DOS" when they mean MS-DOS, although there have in fact been a number of non-Microsoft operating systems also called DOS (such as Apple II DOS). PC-DOS refers to the specific variety of MS-DOS that was licensed by Microsoft to IBM for use on its personal computers, while MS-DOS is the generic version that ran on a wide variety of "PC clones" or "compatibles". Microsoft originally got MS-DOS from another company called Seattle Computer Products which had created its predecessor as an imitation of CP/M. The first version of MS-DOS didn't even support subdirectories, but this was added in version 2.0. Windows runs on a base of MS-DOS, something that was clearly visible in early versions up to 3.11 (where you had to first boot DOS and then run Windows as a separate program), but obscured in later versions (up to and including Windows ME) which boot directly into Windows, but DOS is still there under the hood.
Of particular interest to DOS users is FreeDOS, which reimplements and extends MS-DOS and other DOSs.