AMD64 is 99% the same with the Intel-64 Architecture. It's called AMD64 because AMD was faster than Intel in delivering. (And to Avoid confusion with IA-64 (Itanium)).

You can use a 32 and a 64 Bit Operating System on them (but you are limited to 4GB of Adressable Memory in 32 Bit Systems)

You can run a 32Bit Application on a 64 Bit OS, but you can't run a 64 Bit Application on a 32Bit Operating System.

Processors supporting 64 Bit:

Intel: Some Pentium 4, all since Core2Duo and Core2Duo based Celerons, some Atoms
AMD: All Processors since AMD64

64Bit Architecture has the Advantage of using more than 4GB of Memory and some improvements on the executing of Code. As disadvantage the System is a bit slower (while running 64 Bit OS because you need more Ressources to manage Memory).

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