x86_64 is the name of an architecture, not a either or designation. Here's an explanation of the CPU architectures in relation to DS' vernacular:
x86 - Equivalent to i386, i586, x86 compilations of Linux distros. The good ole' 32-bit chips.
x64 - Equivalent to x86_64 and EM64 (Intel's version) compilations of Linux distros. This is AMD's 64-bit extensions to the x86 architecture which intel later adopted. This is also what is most commonly referred to when every you think of 64-bit chips.
http://en.wikipedia.org/wiki/X86_64
IA64 - This is Intel's 64-bit architecture also referred to as Itanium and is much less common than x86_64. Usually you will only find these in certain HP machines today.
http://en.wikipedia.org/wiki/Itanium