x86 could be viewed as related to a 32 bit version of something.
x64 could be viewed as related to a 64 bit version of something.
Both WinXP and Vista are available as 32 bit and 64 bit versions.
A current generation Intel or AMD processor, can run either a
32 bit or 64 bit OS. But an older processor (like my Pentium 4
or my AthlonXP), can only run the 32 bit version of the OS.
The 64 bit version of OS, is also backward compatible with older
programs, and if it didn't do that at least, it would be a very
lonely OS. What that means is, if you have a 64 bit capable processor,
you can use a 64 bit OS, but run that old 32 bit version of Photoshop
you've always used.
http://en.wikipedia.org/wiki/X86
http://en.wikipedia.org/wiki/X64
Paul