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 was still there under the hood; finally with Windows NT and later systems built on it such as Windows XP and its successors, the low-level operating system kernel was fully integrated to a system that was "Windows" from top to bottom.
Of particular interest to DOS users is FreeDOS, which reimplements and extends MS-DOS and other DOSs.