There are certainly some differences. DOS is a a category of operating system, albeit a very old and simple one (compared to today). MS-DOS was the Microsoft version, although there were several others. Since it did more than run commands (dir, cls, etc.) which is what the command prompt does, I'd say they are different.
On a somewhat related note, some machines at one of the buildings my dad inspects still use MS-DOS to run their security system.
Assume that everything I say is or could be a lie.