Which packages should install for Architectures EM64T® , x86-64 , ia32 , IA64 , Intel®64 , x86 , amd64 , amd32 , Mach64 ?
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In practice, on modern Windows and GNU/Linux, the following are indistinguishable (meaning, if your system claims to support at least one of these, the same software will run on these):
Likewise for these:
IA64 is "Itanium", which is a totally different architecture that is not in any way related to any of the above.
Also, all modern CPUs that support the first group (amd64, etc.) also support code compiled for the second group (x86, etc.) because 64-bit CPUs can execute 32-bit code in a sort of compatibility mode.
There's also an x32 architecture, which is a very new development in software and currently only supported on GNU/Linux, which uses 32-bit addresses, with the 64-bit (amd64) architecture.
So, throwing out all the marketing terminology, what we really have as far as distinct software compatibility environments is: