What's win32 and 64-Bit?

Win32 would refer to any 32-bit Windows related things - like 32-Bit OSes, 32-Bit APIs etc. 64-Bit is a general reference to any 64-Bit things like 64-Bit OSes & APIs etc.

Windows 2000 Professional, Windows XP Professional, Windows Server 2003 are all 32-Bit OSes - unless 64 Bit appears in the title, e.g.:

Windows XP Professional 64 Bit (x64) (for 64-Bit AMD CPUs)
Windows XP Professional 64 Bit (IA64) (for Intel's 64-Bit Itanium CPU)
Windows 2003 Server 64-Bit etc. etc.

... does this clear up the confusion or...?

Win32 is the API set that was introduced with WinNT as a transition to 32-bit code, used in Win95 and lives as the Windows API to today.

64-bit Windows has the Win32 API at its core, with pointer sizes (and pointer sized things) increased to 64-bits, but otherwise the API is intact. There is no Win64 API. It is an unfortunate artifact of naming that the Win32 API is at the heart of writing 64-bit unmanaged code, but that is history for you.

The managed frameworks are driving twoards what is being referred to as WinFX which is the frameworks of the future. It is designed for managed code and will be platform agnostic.

-josh