WinME is a continuation of the Win9x line, which still contains legacy 16-bit code and is still essentially sitting on top of DOS (although it is well hidden in WinME).
Win2K is a continuation of the WinNT line, which is entirely 32-bit code, and does not contain or sit on top of DOS.
WinME is supposed to have the largest compatibility; it is aimed at consumer systems. It can play games without problems.
Win2K, while having far better compatibility than WinNT, still has less compatibility with hardware than WinME. It is aimed at the business environment, has security features and not all games can be played.
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